Nemoto Koji

Faculty of Science　Physics　Condensed Matter PhysicsProfessor
Last Updated :2025/01/11

■Researcher basic information

Degree

  • Doctor of Science, Hokkaido University

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J-Global ID

Research Keyword

  • カスケード模型
  • ランダムネットワーク
  • パーコレーション転移
  • 複雑ネットワーク
  • スピングラス
  • モンテカルロシミュレーション
  • モード解析
  • ランダムスピン系
  • レプリカ交換法
  • エイジング現象
  • EA模型
  • スピングラス・強磁性転移
  • 平均場理論
  • 細胞
  • 境界
  • LCA
  • 双晶変形
  • カオス
  • スピングラスの平均場理論
  • 階層的自由エネルギー構造
  • ガラス的な系
  • イジングモデル

Research Field

  • Natural sciences, Mathematical physics and basic theory

■Career

Career

  • 2014 - Present
    Hokkaido University, Faculty of Science, 教授
  • 2007 - 2013
    Hokkaido University, Faculty of Science, 准教授
  • 1994 - 2007
    北海道大学 大学院理学研究科, 助教授
  • 1993 - 1994
    University of Tsukuba, Institute of Physics, 講師
  • 1989 - 1993
    University of Tsukuba, Institute of Physics, 助手

■Research activity information

Papers

  • Approximate master equations for the spatial public goods game
    Yu Takiguchi, Koji Nemoto
    Physical Review E, 109, 2, American Physical Society (APS), 12 Feb. 2024
    Scientific journal
  • Sudden spreading of infections in an epidemic model with a finite seed fraction
    Takehisa Hasegawa, Koji Nemoto
    European Physical Journal B, 91, 3, Springer Heidelberg, 01 Mar. 2018, [Peer-reviewed]
    English, Scientific journal, We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates for the case with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small.
  • Theoretical Analysis of Bistability in Kuramoto Model with Connectivity-Frequency Correlations
    Toshiki Nagasaki, Satoru Tokuda, Koji Nemoto, Masato Okada
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 87, 1, 014004, PHYSICAL SOC JAPAN, Jan. 2018, [Peer-reviewed]
    English, Scientific journal, One of the interesting features of discontinuous transitions in coupled oscillators is the existence of bistability between two steady states. In this study, we theoretically analyze the Kuramoto model with the following two conditions: (i) the correlation between the connectivity of networks and the natural frequency distribution and (ii) the bimodality of natural frequency distribution. We show that the two conditions induce bistability and how each condition affects the appearance of bistability.
  • Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks
    Takehisa Hasegawa, Koji Nemoto
    PHYSICAL REVIEW E, 96, 2, AMER PHYSICAL SOC, Aug. 2017, [Peer-reviewed]
    English, Scientific journal, This study focuses on investigating the manner in which a prompt quarantine measure suppresses epidemics in networks. A simple and ideal quarantine measure is considered in which an individual is detected with a probability immediately after it becomes infected and the detected one and its neighbors are promptly isolated. The efficiency of this quarantine in suppressing a susceptible-infected-removed (SIR) model is tested in random graphs and uncorrelated scale-free networks. Monte Carlo simulations are used to show that the prompt quarantine measure outperforms random and acquaintance preventive vaccination schemes in terms of reducing the number of infected individuals. The epidemic threshold for the SIR model is analytically derived under the quarantine measure, and the theoretical findings indicate that prompt executions of quarantines are highly effective in containing epidemics. Even if infected individuals are detected with a very low probability, the SIR model under a prompt quarantine measure has finite epidemic thresholds in fat-tailed scale-free networks in which an infected individual can always cause an outbreak of a finite relative size without any measure. The numerical simulations also demonstrate that the present quarantine measure is effective in suppressing epidemics in real networks.
  • Local cluster-size statistics in the critical phase of bond percolation on the Cayley tree
    Tomoaki Nogawa, Takehisa Hasegawa, Koji Nemoto
    JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, IOP PUBLISHING LTD, May 2016, [Peer-reviewed]
    English, Scientific journal, We study bond percolation of the Cayley tree (CT) by focusing on the probability distribution function (PDF) of a local variable, namely, the size of the cluster including a selected vertex. Because the CT does not have a dominant bulk region, which is free from the boundary effect, even in the large-size limit, the phase of the system on it is not well defined. We herein show that local observation is useful to define the phase of such a system in association with the well-defined phase of the system on the Bethe lattice, that is, an infinite regular tree without boundary. Above the percolation threshold, the PDFs of the vertex at the center of the CT (the origin) and of the vertices near the boundary of the CT (the leaves) have different forms, which are also dissimilar to the PDF observed in the ordinary percolating phase of a Euclidean lattice. The PDF for the origin of the CT is bimodal: a decaying exponential function and a system-size-dependent asymmetric peak, which obeys a finite-size-scaling law with a fractal exponent. These modes are respectively related to the PDFs of the finite and infinite clusters in the nonuniqueness phase of the Bethe lattice. On the other hand, the PDF for the leaf of the CT is a decaying power function. This is similar to the PDF observed at a critical point of a Euclidean lattice but is attributed to the nesting structure of the CT around the boundary.
  • Outbreaks in susceptible-infected-removed epidemics with multiple seeds
    Takehisa Hasegawa, Koji Nemoto
    PHYSICAL REVIEW E, 93, 3, AMER PHYSICAL SOC, Mar. 2016, [Peer-reviewed]
    English, Scientific journal, We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an infinitesimal fraction of seeds. However, there have been few studies of epidemic models with finite fractions of seeds. The aim of this paper is to clarify what happens in phase transitions in such cases. The SIR model in networks exhibits two percolation transitions. We derive the percolation transition points for the SIR model with multiple seeds to show that as the infection rate increases epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak.
  • Discontinuous transition of a multistage independent cascade model on networks
    Takehisa Hasegawa, Koji Nemoto
    JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, P11024, IOP PUBLISHING LTD, Nov. 2014, [Peer-reviewed]
    English, Scientific journal, We propose a multistage version of the independent cascade model, which we call a multistage independent cascade (MIC) model, on networks. This model is parameterized by two probabilities: the probability T-1 that a node adopting a fad increases the awareness of a neighboring susceptible node and the probability T-2 that an adopter directly causes a susceptible node to adopt the fad. We formulate a tree approximation for the MIC model on an uncorrelated network with an arbitrary degree distribution p(k). Applied on a random regular network with degree k = 6, this model exhibits a rich phase diagram, including continuous and discontinuous transition lines for fad percolation and a continuous transition line for the percolation of susceptible nodes. In particular, the percolation transition of fads is discontinuous (continuous) when T-1 is larger (smaller) than a certain value. A similar discontinuous transition is observed in random graphs and scale-free networks. Furthermore, assigning a finite fraction of initial adopters dramatically changes the phase boundaries.
  • Critical Phase in Complex Networks: a Numerical Study
    Takehisa Hasegawa, Tomoaki Nogawa, Koji Nemoto
    Discontinuity, Nonlinearity, and Complexity, 01 Oct. 2014, [Peer-reviewed]
    English
  • Hierarchical scale-free network is fragile against random failure
    Takehisa Hasegawa, Koji Nemoto
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 88, 6, 062807.1-062807.5, 06 Dec. 2013, [Peer-reviewed]
    English, Scientific journal, We investigate site percolation in a hierarchical scale-free network known as the Dorogovtsev-Goltsev-Mendes network. We use the generating function method to show that the percolation threshold is 1, i.e., the system is not in the percolating phase when the occupation probability is less than 1. The present result is contrasted to bond percolation in the same network of which the percolation threshold is zero. We also show that the percolation threshold of intentional attacks is 1. Our results suggest that this hierarchical scale-free network is very fragile against both random failure and intentional attacks. Such a structural defect is common in many hierarchical network models. © 2013 American Physical Society.
  • Hierarchical scale-free network is fragile against random failure
    Takehisa Hasegawa, Koji Nemoto
    PHYSICAL REVIEW E, 88, 6, AMER PHYSICAL SOC, Dec. 2013, [Peer-reviewed]
    English, Scientific journal, We investigate site percolation in a hierarchical scale-free network known as the Dorogovtsev-Goltsev-Mendes network. We use the generating function method to show that the percolation threshold is 1, i.e., the system is not in the percolating phase when the occupation probability is less than 1. The present result is contrasted to bond percolation in the same network of which the percolation threshold is zero. We also show that the percolation threshold of intentional attacks is 1. Our results suggest that this hierarchical scale-free network is very fragile against both random failure and intentional attacks. Such a structural defect is common in many hierarchical network models.
  • Profile and scaling of the fractal exponent of percolations in complex networks
    T. Hasegawa, T. Nogawa, K. Nemoto
    EPL, 104, 1, 16006, EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY, Oct. 2013, [Peer-reviewed]
    English, Scientific journal, We propose a novel finite-size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite-order transition with inverted Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical simulations to determine the transition point precisely. Since the neighbor of the ordered phase is not a simple disordered phase but a critical phase, conventional finite-size scaling technique does not work. In our finite-size scaling, the forms of the scaling functions for the order parameter and the fractal exponent determine the transition point and critical exponents numerically for an infinite-order transition as well as a standard second-order transition. We confirm the validity of our scaling hypothesis through Monte Carlo simulations for bond percolations in some network models: the decorated (2,2)-flower and the random attachment growing network, where an infinite-order transition occurs, and the configuration model, where a second-order transition occurs. Copyright (C) EPLA, 2013
  • Robustness of correlated networks against propagating attacks
    T. Hasegawa, K. Konno, K. Nemoto
    EUROPEAN PHYSICAL JOURNAL B, 85, 8, SPRINGER, Aug. 2012
    English, Scientific journal, We investigate robustness of correlated networks against propagating attacks modeled by a susceptible-infected-removed model. By Monte-Carlo simulations, we numerically determine the first critical infection rate, above which a global outbreak of disease occurs, and the second critical infection rate, above which disease disintegrates the network. Our result shows that correlated networks are robust compared to the uncorrelated ones, regardless of whether they are assortative or disassortative, when a fraction of infected nodes in an initial state is not too large. For large initial fraction, disassortative network becomes fragile while assortative network holds robustness. This behavior is related to the layered network structure inevitably generated by a rewiring procedure we adopt to realize correlated networks.
  • Generalized scaling theory for critical phenomena including essential singularity and infinite dimensionality
    Tomoaki Nogawa, Takehisa Hasegawa, Koji Nemoto
    Phys. Rev. Lett. 108 (2012) 255703, 108, 25, 255703, 255703, American Physical Society, 22 Jun. 2012, [Peer-reviewed]
    English, Scientific journal, We propose a generic scaling theory for critical phenomena that includes

    power-law and essential singularities in finite and infinite dimensional

    systems. In addition, we clarify its validity by analyzing the Potts model in a

    simple hierarchical network, where a saddle-node bifurcation of the

    renormalization-group fixed point governs the essential singularity.
  • Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network
    Tomoaki Nogawa, Takehisa Hasegawa, Koji Nemoto
    Phys. Rev. E 86, 030102(R) (2012), 86, 3, 30102, 30102, American Physical Society, 22 Jun. 2012, [Peer-reviewed]
    English, Scientific journal, We study the Ising model in a hierarchical small-world network by

    renormalization group analysis, and find a phase transition between an ordered

    phase and a critical phase, which is driven by the coupling strength of the

    shortcut edges. Unlike ordinary phase transitions, which are related to

    unstable renormalization fixed points (FPs), the singularity in the ordered

    phase of the present model is governed by the FP that coincides with the stable

    FP of the ordered phase. The weak stability of the FP yields peculiar

    criticalities including logarithmic behavior. On the other hand, the critical

    ...
  • Phase transition without global ordering in a hierarchical scale-free network
    Takehisa Hasegawa, Masataka Sato, Koji Nemoto
    PHYSICAL REVIEW E, 85, 1, AMER PHYSICAL SOC, Jan. 2012, [Peer-reviewed]
    English, Scientific journal, We study the site-bond percolation on a hierarchical scale-free network, namely, the decorated (2,2)-flower, by using the renormalization group technique. The phase diagram essentially depends on the fraction of occupied sites. Surprisingly, when each site is unoccupied even with a small probability, the system permits neither the percolating phase nor the nonpercolating phase, but rather only critical phases. Although the order parameter always remains zero, a transition still exists between the critical phases that is characterized by the value of the fractal exponent, which measures the degree of criticality; the system changes from one critical state to another with the jump of the fractal exponent at the transition point. The phase boundary depends on the fraction of occupied sites. When the fraction of unoccupied sites exceeds a certain value, the transition line between the critical phases disappears, and a unique critical phase remains.
  • Generating-function approach for bond percolation in hierarchical networks
    Takehisa Hasegawa, Masataka Sato, Koji Nemoto
    PHYSICAL REVIEW E, 82, 4, AMER PHYSICAL SOC, Oct. 2010, [Peer-reviewed]
    English, Scientific journal, We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts (p) over tilde and that of the ordinary bonds p. The system has a critical phase in which the percolating probability P takes an intermediate value 0 < P < 1. Using generating function approach, we calculate the fractal exponent psi of the root clusters to show that psi varies continuously with (p) over tilde in the critical phase. We confirm numerically that the distribution n(s) of cluster size s in the critical phase obeys a power law n(s)proportional to s(-tau), where tau satisfies the scaling relation tau = 1+psi(-1). In addition the critical exponent beta((p) over tilde) of the order parameter varies as (p) over tilde, from beta similar or equal to 0.164 694 at (p) over tilde = 0 to infinity at (p) over tilde = (p) over tilde(c)=5/32.
  • Critical phase of bond percolation on growing networks
    Takehisa Hasegawa, Koji Nemoto
    PHYSICAL REVIEW E, 81, 5, AMER PHYSICAL SOC, May 2010, [Peer-reviewed]
    English, Scientific journal, The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size N as N(psi) and the mean number of clusters with size s per node follows a power function n(s)proportional to s(-tau) in the whole range of open bond probability p. The exponent tau and the fractal exponent psi are also derived as a function of p and the degree exponent gamma and are found to satisfy the scaling relation tau=1 + psi(-1). Numerical results with several network sizes are quite well fitted by a finite-size scaling for a wide range of p and gamma, which gives a clear evidence for the existence of a critical phase.
  • Ferromagnetic Ising spin systems on the growing random tree
    Takehisa Hasegawa, Koji Nemoto
    PHYSICAL REVIEW E, 80, 2, AMER PHYSICAL SOC, Aug. 2009, [Peer-reviewed]
    English, Scientific journal, We analyze the ferromagnetic Ising model on a scale-free tree; the growing random tree model with the linear attachment kernel A(k)=k+alpha. We derive an estimate of the divergent temperature T(s) below which the zero-field susceptibility of the system diverges. Our result shows that T(s) is related to alpha as tanh(J/T(s))=alpha/[2(alpha+1)], where J is the ferromagnetic interaction. An analysis of exactly solvable limit for the model and numerical calculation supports the validity of this estimate.
  • Abnormal Diffusion of Single Vortex in Two-Dimensional XY Model
    Tomoaki Nogawa, Koji Nemoto
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 78, 6, PHYSICAL SOC JAPAN, Jun. 2009, [Peer-reviewed]
    English, Scientific journal, We study the thermal diffusion dynamics of a single vortex in a two-dimensional XY model. By numerical simulations, we find an abnormal diffusion such that the mobility decreases with time t as 1/ln t. In addition, we construct a one-dimensional diffusion-like equation to model the dynamics and confirm that it conserves the quantitative property of the abnormal diffusion. By analyzing the reduced model, we find that the radius of the collectively moving region together with the vortex core increases as R(t) alpha t(1/2). This suggests that the mobility of the vortex is described by the dynamical correlation length as 1/ln R(t).
  • Spatiotemporal scaling for out-of-equilibrium relaxation dynamics of an elastic manifold in random media: Crossover between diffusive and glassy regimes
    Tomoaki Nogawa, Koji Nemoto, Hajime Yoshino
    PHYSICAL REVIEW B, 77, 6, AMER PHYSICAL SOC, Feb. 2008, [Peer-reviewed]
    English, Scientific journal, We study the relaxation dynamics of a three-dimensional elastic manifold in a random potential from a uniform initial condition by numerically solving the Langevin equation. We observe the growth of the roughness of the system up to larger wavelengths with time. We analyze the structure factor in detail and find a compact scaling ansatz describing two distinct time regimes and the crossover between them. We find that a short-time regime corresponding to a length scale smaller than the Larkin length L(c) is well described by the Larkin model, which predicts a power-law growth of the domain size L(t). Longer-time behavior exhibits a glassy regime with slower growth of L(t).
  • Susceptibility of the Ising model on the scale-free network with a Cayley tree-like structure
    Takehisa Hasegawa, Koji Nemoto
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 387, 5-6, 1404, 1410, ELSEVIER SCIENCE BV, Feb. 2008, [Peer-reviewed]
    English, Scientific journal, We derive the exact expression for the zero-field susceptibility of each spin of the Ising model on the scale-free (SF) network having the degree distribution P(k) alpha k(-gamma) with the Cayley tree-like structure. The system shows that: (i) the zero-field susceptibility of a spin in the interior part diverges below the transition temperature of the SF network with the Bethe lattice-like structure T-c for gamma > 3, while it diverges at any finite temperature for gamma <= 3, and (ii) the surface part diverges below the divergence temperature of the SF network with the Cayley tree-like structure T-s for gamma > 3, while it diverges at any finite temperature for y <= 3. (c) 2007 Elsevier B.V. All rights reserved.
  • Spatio-temporal scaling for out-of-equilibrium relaxation dynamics of an elastic manifold in random media: crossover between the Larkin regime and thermally activated regime
    Tomoaki Nogawa, Koji Nemoto, Hajime Yoshino
    Phys. Rev. B 77 (2008) 064204, 77, 6, 10 Oct. 2007, [Peer-reviewed]
    Scientific journal, We study relaxation dynamics of a three dimensional elastic manifold in

    random potential from a uniform initial condition by numerically solving the

    Langevin equation.We observe growth of roughness of the system up to larger

    wavelengths with time.We analyze structure factor in detail and find a compact

    scaling ansatz describing two distinct time regimes and crossover between them.

    We find short time regime corresponding to length scale smaller than the Larkin

    length $L_c$ is well described by the Larkin model which predicts a power law

    growth of domain size $L(t)$. Longer time behavior exhi...
  • The melting transition of a vortex lattice in the uniformly frustrated XY model with quasi-one-dimensional and quasi-two-dimensional coupling anisotropy
    T. Nogawa, K. Nemoto
    JOURNAL OF PHYSICS-CONDENSED MATTER, 19, 14, IOP PUBLISHING LTD, Apr. 2007, [Peer-reviewed]
    English, Scientific journal, The uniformly frustrated XY model on the cubic lattice with an anisotropic coupling constant is studied numerically. Quasi-one-dimensional and quasi-two-dimensional systems are examined as models for a charge density wave in a ring crystal and a layer superconductor, respectively. The melting transition of a vortex lattice is investigated by means of non-equilibrium relaxation analysis. We find scaling behaviour of the relaxation with a power law, which indicates that the phase transition is of second order, in contrast to the first-order transition in the isotropic case. The critical exponents are estimated as beta = 0.28 and z nu = 2.3 for the quasi-one-dimensional system and beta = 0.40 and z nu = 2.9 for the quasi-two-dimensional system, and alpha approximate to 0 for both cases. This implies that the universality classes of the two are different.
  • Ising model on the scale-free network with a Cayley-tree-like structure
    Takehisa Hasegawa, Koji Nemoto
    PHYSICAL REVIEW E, 75, 2, AMERICAN PHYSICAL SOC, Feb. 2007, [Peer-reviewed]
    English, Scientific journal, We derive an exact expression for the magnetization and the zero-field susceptibility of the Ising model on a random graph with degree distribution P(k)proportional to k(-gamma) and with a boundary consisting of leaves, that is, vertices whose degree is 1. The system has no magnetization at any finite temperature, and the susceptibility diverges below a certain temperature T-s depending on the exponent gamma. In particular, T-s reaches infinity for gamma <= 4. These results are completely different from those of the case having no boundary, indicating the nontrivial roles of the leaves in the networks.
  • Real space renormalization group analysis with the replica method for the two dimensional Ising Edwards-Anderson model
    Takehisa Hasegawa, Koji Nemoto
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 75, 7, PHYSICAL SOC JAPAN, Jul. 2006, [Peer-reviewed]
    English, Scientific journal, We apply the real space renormalization group (RG) to the replica Hamiltonian of the two dimensional Ising Edwards-Anderson model to discuss the existence of the spin glass (SG) phase. We derive the RG equations under the replica symmetric (RS) ansatz and the resulting flow diagram indicates the existence of the SG phase. The critical exponent for the SG transition has a plausible value while that of the multicritical point (MCP) is a complex number. We consider that this failure at the MCP is due to not taking the RS breaking into account. Indeed we find that the RS breaking parameter is relevant both at the SG critical point and the MCP, indicating the nontriviality of the SG phase of this model.
  • Nonequilibrium relaxation analysis of a quasi-one-dimensional frustrated XY model for charge-density waves in ring-shaped crystals
    T Nogawa, K Nemoto
    PHYSICAL REVIEW B, 73, 18, AMERICAN PHYSICAL SOC, May 2006
    English, Scientific journal, We propose a model for charge-density waves in ring-shaped crystals, which depicts frustration between intra- and interchain couplings coming from cylindrical bending. It is then mapped to a three-dimensional uniformly frustrated XY model with one-dimensional anisotropy in connectivity. The nonequilibrium relaxation dynamics is investigated by Monte Carlo simulations to find a phase transition which is quite different from that of usual whisker crystal. We also find that the low-temperature state is a three-dimensional phase vortex lattice with a two-dimensional phase coherence in a cylindrical shell and the system shows power-law relaxation in the ordered phase.
  • Ordered phase of dipolar spin ice under [110] magnetic field
    S Yoshida, K Nemoto, K Wada
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 73, 7, 1619, 1622, PHYSICAL SOC JAPAN, Jul. 2004
    English, Scientific journal, We found that the true ground state of a dipolar spin ice system under a [110] magnetic field is a "Q = X" structure, which is consistent with both experiments and Monte Carlo simulations. We performed a Monte Carlo simulation to confirm the existence of a first-order phase transition under a [110] magnetic field. The result indicates the existence of the first-order phase transition to the "Q = X" phase in a magnetic field above 0.35 T for Dy2Ti2O7. In this letter we show a magnetic field-temperature phase diagram to summarize the ordered states of this system.
  • Symmetry, complexity and multicritical point of the two-dimensional spin glass
    Jean-Marie Maillard, Koji Nemoto, Hidetoshi Nishimori
    Journal of Physics A: Mathematical and General, 36, 38, 9799, 9825, 26 Sep. 2003
    English, Scientific journal, We analyse models of spin glasses on the two-dimensional square lattice by exploiting symmetry arguments. The replicated partition functions of the Ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge Boltzmann factors. It is shown that the applications of homogeneous and Hadamard inverses to the edge Boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions, suggesting that the system has special simplicities under such conditions. Using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram.
  • Duality and multicritical point of two-dimensional spin glasses
    H Nishimori, K Nemoto
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 321, 1-2, 108, 113, ELSEVIER SCIENCE BV, Apr. 2003, [Peer-reviewed]
    English, Scientific journal, We present a conjecture on the exact location of the multicritical point of models of spin glasses on the two-dimensional square lattice using duality trails formal ion. The results not only agree very well with numerical estimates but also conform excellently to the existing knowledge on annealed systems and to the arguments Using gauge symmetry. (C) 2002 Elsevier Science B.V. All rights reserved.
  • Duality and multicritical point of two-dimensional spin glasses
    H Nishimori, K Nemoto
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 71, 4, 1198, 1199, PHYSICAL SOC JAPAN, Apr. 2002
    English, Scientific journal, Determination of the precise location of the multicritical point and phase

    boundary is a target of active current research in the theory of spin glasses.

    In this short note we develop a duality argument to predict the location of the

    multicritical point and the shape of the phase boundary in models of spin

    glasses on the square lattice.
  • Application of the cluster variation method to spin ice systems on the pyrochlore lattice
    S Yoshida, K Nemoto, K Wada
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 71, 3, 948, 954, PHYSICAL SOC JAPAN, Mar. 2002
    English, Scientific journal, The cactus approximation in the cluster variation method is applied to the spin ice system with nearest neighbor ferromagnetic coupling. The temperature dependences of the entropy and the specific heat show qualitatively good agreement with those observed by Monte Carlo simulations and experiments, and the Pauling value is reproduced for the residual entropy. The analytic expression of the q-dependent magnetic susceptibility is obtained, from which the absence of magnetic phase transition is confirmed. The neutron scattering pattern is also evaluated and found to be consistent with that obtained from Monte Carlo simulations.
  • Numerical Study of Aging in the Generalized Random Energy Model
    Sasaki Munetaka, Nemoto Koji
    J Phys Soc Jpn, 70, 4, 1099, 1104, The Physical Society of Japan (JPS), 15 Apr. 2001
    English, Magnetizations are introduced to the Generalized Random Energy Model (GREM) and numerical simulations on ac susceptibility is made for direct comparison with experiments in glassy materials. Prominent dynamical natures of spin glasses, i.e., memory effect and reinitialization, are reproduced well in the GREM. The existence of many layers causing continuous transitions is very important for the two natures. Results of experiments in other glassy materials such as polymers, supercooled glycerol and orientational glasses, which are contrast to those in spin glasses, are interpreted well by the Single-layer Random Energy Model.
  • Analysis on Aging in the Generalized Random Energy Model
    Sasaki Munetaka, Nemoto Koji
    J Phys Soc Jpn, 69, 9, 3045, 3050, The Physical Society of Japan (JPS), 15 Sep. 2000
    English, A new dynamics more natural than that proposed by Bouchaud and Dean is introduced to the Generalized Random Energy Model, and the master equation for the dynamics is solved exactly to calculate the time correlation function C(t+t w,t w) . Although our results are very similar to those obtained by Bouchaud and Dean qualitatively, the exponents for power law relaxation are different. The Zero-Field-Cooled magnetization is also calculated with a relation between the correlation function and the response function which holds even if the relaxation is non-equilibrium. The validity of these analytic results are confirmed by numerical simulations.
  • Scaling Law and Aging Phenomena in the Random Energy Model
    Sasaki Munetaka, Nemoto Koji
    J Phys Soc Jpn, 69, 8, 2642, 2646, The Physical Society of Japan (JPS), 15 Aug. 2000
    English, We study the effect of temperature shift on aging phenomena in the Random Energy Model (REM). From calculation on the correlation function and simulation on the Zero-Field-Cooled magnetization, we find that the REM satisfies a scaling relation even if temperature is shifted. Furthermore, this scaling property naturally leads to results obtained in experiment and the droplet theory.
  • Memory Effect, Rejuvenation and Chaos Effect in the Multi-Layer Random Energy Model
    Sasaki Munetaka, Nemoto Koji
    J Phys Soc Jpn, 69, 7, 2283, 2290, The Physical Society of Japan (JPS), 15 Jul. 2000
    English, We introduce magnetization to the Multi-layer Random Energy Modelwhich has a hierarchical structure, and perform Monte Carlo simulations to observe behavior of ac-susceptibility.We find that this model is able to reproduce three prominent featuresof spin glasses, i.e., memory effect, rejuvenation and chaos effect,which were found recentlyby various experiments on aging phenomena with temperature variations.
  • Aging Phenomena of Magnetization in a Hierarchical Diffusion Model
    Sasaki Munetaka, Nemoto Koji
    J Phys Soc Jpn, 68, 4, 1148, 1161, The Physical Society of Japan (JPS), 15 Apr. 1999
    English, The magnetization is introduced to a hierarchical diffusion model anda relation between the response function and the correlation function is derived to evaluate the zero-field-cooled magnetization (ZFCM) and the thermoremanent magnetization (TRM).It is found that if the correlation of distribution of magnetization (CDM) is weak, the behaviors of ZFCM and TRM are governed by the distribution of the barrier energy.The aging is observed in this case. On the other hand, these behaviors are governed by the strength of CDM if it is strong enough, andthe aging is not observed.
  • Exchange Monte Carlo method and application to spin glass simulations
    K Hukushima, K Nemoto
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 65, 6, 1604, 1608, PHYSICAL SOC JAPAN, Jun. 1996
    English, Scientific journal, We propose an efficient Monte Carlo algorithm for simulating a ''hardly-relaxing'' system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional +/-J Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.
  • Application of an extended ensemble method to spin glasses
    K Hukushima, H Takayama, K Nemoto
    INTERNATIONAL JOURNAL OF MODERN PHYSICS C-PHYSICS AND COMPUTERS, 7, 3, 337, 344, WORLD SCIENTIFIC PUBL CO PTE LTD, Jun. 1996, [Peer-reviewed]
    English, Scientific journal, An efficient Monte Carlo algorithm for simulating hardly-relaxing systems is proposed. By using this algorithm the three-dimensional +/-J Ising spin glass model is studied. The result shows that reasonable values of the critical temperature and of the critical exponents can be obtained within Monte Carlo steps much shorter than the observation time a conventional simulation usually requires.
  • THE SPIN DYNAMICS OF THE 3D+/-J ISING SPIN-GLASS MODEL IN HIGH-TEMPERATURE REGION
    K HUKUSHIMA, K NEMOTO
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 64, 6, 2183, 2190, PHYSICAL SOC JAPAN, Jun. 1995
    English, Scientific journal, We study the spin dynamics of the 3D +/- J Ising model in high temperatures. The spin autocorrelation function can be expressed in terms of the eigenvalues of the interaction matrix in the high temperature limit. We obtain the true asymptotic behavior by evaluating the eigenvalues and find that the short time behavior is well described by the stretched exponential law.
  • A MONTE-CARLO STUDY ON THE SPIN DYNAMICS OF THE 2D+/-J ISING SPIN-GLASS MODEL
    K HUKUSHIMA, K NEMOTO
    JOURNAL OF PHYSICS-CONDENSED MATTER, 5, 9, 1389, 1398, IOP PUBLISHING LTD, Mar. 1993, [Peer-reviewed]
    English, Scientific journal, The examine the dynamical properties of the 2D +/- J Edwards-Anderson Ising spin glass in the anomalous phase which corresponds to the Griffiths phase in the diluted ferromagnetic system. By using Monte Carlo simulation we find that the autocorrelation function can be described as a function of a power of scaled time. This new scaling includes both the stretched exponential law for the intermediate stage and the logarithmic law for the early stage of relaxation. The relaxation time obtained from the scaling is found to diverge exponentially with exponent proportional to T-2.
  • RELAXATIONAL DYNAMICS IN 2D-ISING AND 3D-ISOTROPIC HEISENBERG SPIN-GLASSES
    K HUKUSHIMA, H YOSHINO, K NEMOTO, H TAKAYAMA
    COMPUTER AIDED INNOVATION OF NEW MATERIALS II, PTS 1 AND 2, 403, 406, ELSEVIER SCIENCE PUBL B V, 1993, [Peer-reviewed]
    English, International conference proceedings
  • Dynamical Mean Field Theory of Spin Glasses and Their Phase Transitions in ac External Fields :
    TAKAYAMA Hajime, SHIRAKURA Takayuki, NEMOTO Koji
    Progress of theoretical physics. Supplement, 87, 191, 213, Progress of Theoretical Physics, 1987
    English, The dynamical mean field theory of spin glasses is investigated in systems with non-zero mean of the infinitely-ranged random exchange interactions under uniform but alternating external magnetic fields. A perturbational expansion with respect to the interaction uσ^4_i introduced in a soft-spin version of the model is analyzed by means of the diagrammatic method. Restricting ourselves to its lowest order (single-loop) approximation, we examine relaxational dynamics of the model spin glass and clarify nature of its phase transition in the presence of an ac external field. The results provide a new clue to ac nonlinear measurements on spin glasses.
  • On the Transverse Nonlinear Susceptibility of the Vector SK Spin Glass in a Finite Field
    Koji NEMOTO, Hajime TAKAYAMA, Department of Phisics Hokkaido University, Research Institute for Fundamental Phisics Kyoto University
    Progress of theoretical physics = Progress of theoretical physics, 75, 2, 448, 450, Published for the Research Institute for Fundamental Physics by Physical Society of Japan, 25 Feb. 1986
    English, It is shown that the static transverse nonlinear susceptibility of the isotropic m-vector SK spin glass does not diverge on the Gabay-Toulouse line as long as a finite longitudinal field is applied. In connection with this result, some arguments on the recent theoretical and experimental work are presented.
  • Monte Carlo Study on the 2D $\pm J$ Ising Spin Glass —Dynamical Behavior of Individual Spins and Spin Clusters—
    Nemoto Koji, Matsukawa Hiroshi, Takayama Hajime
    J Phys Soc Jpn, 51, 10, 3126, 3135, The Physical Society of Japan (JPS), 15 Oct. 1982
    English, We study the Monte Carlo simulation on the two-dimensional $\pm J$ Ising spin glass aiming to clarify the relation between behavior of individual spins and spin clusters in each sample and common spin glass properties of the system. Particularly relaxation times of individual spins are evaluated and their temperature dependences are examined. Making use of data obtained, we discuss in detail spin-freezing process in this model for spin glass. One of our most interesting findings is that spin relaxation processes at temperatures $T{\gtrsim}0.8J$ obey Fulcher's law with $T_{0},{\simeq}0.5J$, implying that the characteristic relaxation time of the system may diverge at $T_{0}$.

Other Activities and Achievements

Research Themes

  • Master equations for epidemic dynamics in networks
    Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
    Apr. 2016 - Mar. 2020
    Nemoto Koji
    The behavior of the SWIR infection model with finite seed ratio (initially infected person) was analyzed on a regular random graph by numerical analysis of AME (approximate master equation), and the existence of two critical infection rates was clarified. In addition, a model that introduced quarantine measures to the SIR infection model on regular random and scale-free networks is proposed, and the superiority to random vaccine measures is clarified. Furthermore, both SWIS and SWSIS models, which are extensions of the SIS model, are examined in a unified manner, and the mechanism of continuous phase transition and discontinuous phase transition that appear in the finite seed ratio variation is clarified.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, 16K05507
  • multiple phase transition of probabilistic models on non-Euclidean graphs
    Grants-in-Aid for Scientific Research
    01 Apr. 2015 - 31 Mar. 2018
    Hasegawa Takehisa, Nemoto Koji, Nogawa Tomoaki, Iwase Yuta, Ukita Yuki
    It is known that mathematical models placed on non-Euclidean graphs, e.g. complex networks and nonamenable graphs, often exhibit novel phase transitions, which are never observed in Euclidean systems. In order to unveil the relationship between the structure of networks and phase transitions thereon, we investigated the following topics: (1) the statistical properties of the critical phase for bond percolation (in tree), (2) the origin of the absence of the ordered state for site percolation in hierarchical networks, (3) the characterization of the nonequilibrium multiple phase transitions for the contact process (in tree and Farey graph), and (4) the effect of the initial condition on the phase transitions of the infectious disease models in complex networks.
    Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (B), Ibaraki University, 15K17716
  • Aimed for the elucidation of mechanism of collective multi-cellular migration during 3D morphogenesis
    Grants-in-Aid for Scientific Research
    01 Apr. 2013 - 31 Mar. 2018
    KAWABATA Kazushige
    Construction of 3D structures by multi cellular system, such as blood vessel, clusters of air-exchanging sacks, produces specific functions. To construct 3D structures, cells should move collectively. However, the mechanism of cellular collective movement is not unclear yet. This project is aimed to elucidate mechanism of cellular collective movement by developing cell tracking system, 2D and 3D cellular traction force measurement, cell junction protein-knockout cell lines. In addition, we simulated multi cellular collective movement by making motion equation for cells. Combination of cell tracking system and established knockout cell lines showed that collective movement requires a cell-cell junction protein. The results of computer simulation indicated that important factor is not only cell-cell contact but also cellular modulate elasticity. These findings may be useful to design an intended 3D structure in the field of tissue regeneration.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Hokkaido University, 25287106
  • Mechanical memory effect of cells in colony
    Grants-in-Aid for Scientific Research(基盤研究(B))
    2006 - 2008
    Kazushige KAWABATA, Hisashi HAGA, Koji NEMOTO
    細胞集団がどのように連携・協同して血管や臓器などのマクロな形態を形成するかその機構を解明することを目的に、細胞に蓄積される力学的記憶効果を調べた。本研究では、走査型プローブ顕微鏡を用いた新たな測定装置を構築し、細胞に力学的変形刺激を加えた場合に細胞内に発生する力の応答を調べた。その結果、細胞の変形パターンによって、その後の細胞の力学的応答が大きく異なり、細胞レベルに力学的な記憶効果があることを明らかにした。
    Ministry of Education, Culture, Sports, Science and Technology, 基盤研究(B), 北海道大学, Coinvestigator not use grants, Competitive research funding, 18340122
  • Statistical Physics of Fluctuations in Glassy
    Grants-in-Aid for Scientific Research(国際学術研究, 基盤研究(B))
    1998 - 1999
    Hajime TAKAYAMA, Bouchaud J.P, Campbell I.A, Orbacn R, 根本 幸児, 西森 秀稔
    In this program, by the close collaboration of the researchers in France, US and Japan, as well as of the experimentalists and theorists, the fundamental nature of fluctuation which govern the equilibrium and non-equilibrium dynamics in glassy systems such as spin glasses has been studied. The various subjects in the systems have been individually investigated by the sub-groups (or individual members), and their results have been discussed in the workshops-at Royaumont, France, October 1998, and at Kyoto, October 1999-which all the members participated to look for a common concept(s) on flu...
    Ministry of Education, Culture, Sports, Science and Technology, 国際学術研究, 基盤研究(B), 東京大学, Coinvestigator not use grants, Competitive research funding, 10044064
  • Aging Phenomena in Complex Systems
    Grants-in-Aid for Scientific Research(国際学術研究)
    1996 - 1997
    Hajime TAKAYAMA, Clark W.G, Campbell I, 西森 秀稔, 根本 幸児, 川村 光, 鈴木 増雄, Orbach R, Ocio M, 伊藤 厚子, 都 福仁, Orbach R, Cambell I, Campbell I
    Aging phenomena in random systems with frustration, or complex systems, have been extensively investigated more than a decade. They are infinitely long-time relaxation processes to equilibrium (but in some systems to a state different from equilibrium). Researches on the phenomena are expected to open a new field in statistical physics and condensed matter physics, namely, the out-of -equilibrium dynamics in such complex systems. In the course of this program aging phenomena and their related slow dynamics in spin-glasses were mainly studied. We obtained various interesting findings which p...
    Ministry of Education, Culture, Sports, Science and Technology, 国際学術研究, 東京大学, Coinvestigator not use grants, Competitive research funding, 08044060
  • Chaotic motion of twin boundary in organic single crystals.
    Grants-in-Aid for Scientific Research(基盤研究(B))
    1996 - 1997
    Kazushige KAWABATA, 小野寺 彰, 根本 幸児
    Structure and dynamics of twin boundaries in (TMTSF) _2PF_6 were studied. From microscopic observations, they are planar in shape and their width is less than 10 nm. No change in their shape was found. Their movement and pair annihilation do not leave any trace in the crystal surface. The twin boundary shows complex motion under controlled external force. The twin boundary moves intermittently and its velocity varies from run to run though same measurement was repeated under the same force and within the same area of the crystal. When position dependent velocity of the twin boundary is norm...
    Ministry of Education, Culture, Sports, Science and Technology, 基盤研究(B), 北海道大学, Coinvestigator not use grants, Competitive research funding, 08455048
  • Numerical Analysis of the Clister Effect in Spin Glass Systems
    Grants-in-Aid for Scientific Research(一般研究(C))
    1994 - 1995
    Koji NEMOTO
    There exist many metastable states in randomly frustrated systems such as spin glass. Considering the situation, one expects that most of such systems exhibit glassy relaxations, and in fact, extremely slow dynamics has been found experimentally in many materials. One of the ideas to understand the anomalous relaxation is creation andgrowth of clusters in which spins are highly correlated with each other. The purpose of this research was to reveal how the clusters behaves and how they relate to the anomalous relaxation. Our research was organized as follows :1.In order to understand how the...
    Ministry of Education, Culture, Sports, Science and Technology, 一般研究(C), 北海道大学, Principal investigator, Competitive research funding, 06640498
  • 氷Ih-XI相転移をガラス転移として扱う統計力学的研究
    科学研究費補助金(一般研究(C))
    1994 - 1994
    徳永 正晴, 根本 幸児
    1.Ice ruleの制約下で可能な水素配置の揺らぎをしらべるため,(a)各水素結合上での水素の位置,又は(b)H_2Oの6つの配向間の相関関数のFourier成分を調べている。(1)(a)の立場で,KDPのSlaterモデルにおける中性子臨界散乱の逆格子空間での強度分布の数値計算をワークステーションを使用して行った。Bethe近似で実験とよく似た強度分布が得られた(論文印刷中)(2)x線散乱に主要な役割を果たすOの散乱への寄与を取り入れるため,(b)の立場で6配向回転子間の相関関数をBethe近似で計算した。6x6行列の定式化の計算はワークステーションを使用し,まずSlaterモデルと同じ帯電率が導けることを確かめた。Fourier成分についてKDPで確かめた後,氷に適用して数値計算する。(3)簡単な相関関数の計算方法として,吉森らがFe_3O_4のFe^<+2>とFe^<+3>の配列の問題に適用した方法がある。この方法を氷立方相及びIh相での水素位置間の相関関数のFourier成分の計算に適用して定式化し,数値計算をワークステーションを使用して行っている。2.多くの準安定状態を有するGlass相の平衡状態への緩和時間が,モンテカルロシミュレーションに於いて無限となることを逃げるために拡張アンサンブルの方法が提案されている。これを実際に3次元±J Isingモデルに応用しs...
    文部科学省, 一般研究(C), 北海道大学, Coinvestigator not use grants, Competitive research funding, 06640493
  • Ergodic-NonErgodic Transition Phenomena in Condensed Matters
    Grants-in-Aid for Scientific Research(一般研究(C))
    1989 - 1990
    Hajime TAKAYAMA, 根本 幸児
    Some condensed matters, such as spin glasses, exhibit an Ergodic-nonErgodic transition phenomenon, i. e., their free energy structure in phase space has a unique valley at high temperatures, while it has many valleys at low temperatures with substantial barriers between them. This type of transition phenomena has been first described by the mean-field theory for spin glasses. In the present research project, we have extensively analyzed the naive mean-field (NMF) model by solving its equations of states numerically, and have obtained the following results.1) We introduce a class of mean-fie...
    Ministry of Education, Culture, Sports, Science and Technology, 一般研究(C), 筑波大学, Coinvestigator not use grants, Competitive research funding, 01540298
  • Study of the Ising Models Using Special Purpose Computer System
    Grants-in-Aid for Scientific Research(総合研究(A))
    1988 - 1990
    Masuo SUZUKI, 根本 幸児, 宮下 精二, 香取 真理, 桂 重俊
    The computational physics becomes most important field in modern physics because the computational power has been increasing exponentially and computational study is most effective analyzing method for many important problems. It has been shown that the special purpose computer systems are useful for the theoretical researches. But such systems have not been available unless the researcher constructs one for his study. The main purpose of this research project is to supply such systems to the researchers who need strong simulation power for their studies for the Ising models.The special pur...
    Ministry of Education, Culture, Sports, Science and Technology, 総合研究(A), 東京大学, Coinvestigator not use grants, Competitive research funding, 63302014
  • スピングラスの統計力学的研究
    科学研究費助成事業
    1988 - 1988
    根本 幸児
    日本学術振興会, 奨励研究(A), 東京大学, 63790178

Educational Organization