根本 幸児 (ネモト コウジ)

理学研究院 物理学部門 凝縮系物理学分野教授
Last Updated :2024/12/04

■研究者基本情報

学位

  • 理学博士, 北海道大学

Researchmap個人ページ

研究キーワード

  • 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

研究分野

  • 自然科学一般, 数理物理、物性基礎

■経歴

経歴

  • 2014年 - 現在
    北海道大学 大学院理学研究院, Faculty of Science, 教授
  • 2007年 - 2013年
    北海道大学 大学院理学研究院, Faculty of Science, 准教授
  • 1994年 - 2007年
    北海道大学 大学院理学研究科, 助教授
  • 1993年 - 1994年
    筑波大学 物理学系, Institute of Physics, 講師
  • 1989年 - 1993年
    筑波大学 物理学系, Institute of Physics, 助手

■研究活動情報

論文

  • Approximate master equations for the spatial public goods game
    Yu Takiguchi, Koji Nemoto
    Physical Review E, 109, 2, American Physical Society (APS), 2024年02月12日
    研究論文(学術雑誌)
  • 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, 2018年03月01日, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2018年01月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2017年08月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2016年05月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2016年03月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2014年11月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2014年10月01日, [査読有り]
    英語
  • 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, 2013年12月06日, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2013年12月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2013年10月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2012年08月
    英語, 研究論文(学術雑誌), 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, 2012年06月22日, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2012年06月22日, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2012年01月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2010年10月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2010年05月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2009年08月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2009年06月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2008年02月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2008年02月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2007年10月10日, [査読有り]
    研究論文(学術雑誌), 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, 2007年04月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2007年02月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2006年07月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2006年05月
    英語, 研究論文(学術雑誌), 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, 2004年07月
    英語, 研究論文(学術雑誌), 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, 2003年09月26日
    英語, 研究論文(学術雑誌), 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, 2003年04月, [査読有り]
    英語, 研究論文(学術雑誌), 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, 2002年04月
    英語, 研究論文(学術雑誌), 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, 2002年03月
    英語, 研究論文(学術雑誌), 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
    Journal of the Physical Society of Japan, 70, 4, 1099, 1104, 一般社団法人日本物理学会, 2001年04月15日
    英語, 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
    Journal of the Physical Society of Japan, 69, 9, 3045, 3050, 一般社団法人日本物理学会, 2000年09月15日
    英語, 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
    Journal of the Physical Society of Japan, 69, 8, 2642, 2646, 一般社団法人日本物理学会, 2000年08月15日
    英語, 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
    Journal of the Physical Society of Japan, 69, 7, 2283, 2290, 一般社団法人日本物理学会, 2000年07月15日
    英語, 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
    Journal of the Physical Society of Japan, 68, 4, 1148, 1161, 一般社団法人日本物理学会, 1999年04月15日
    英語, 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, 1996年06月
    英語, 研究論文(学術雑誌), 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, 1996年06月, [査読有り]
    英語, 研究論文(学術雑誌), 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
    Hukushima Koji, Nemoto Koji
    Journal of the Physical Society of Japan, 64, 6, 2183, 2190, 社団法人日本物理学会, 1995年06月
    英語, 研究論文(学術雑誌), 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, 1993年03月, [査読有り]
    英語, 研究論文(学術雑誌), 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年, [査読有り]
    英語, 研究論文(国際会議プロシーディングス)
  • 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年
    英語, 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
    Nemoto Koji, Takayama Hajime, 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, 1986年02月25日
    英語, 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, 一般社団法人日本物理学会, 1982年10月15日
    英語, 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 $T_{0}$.

その他活動・業績

共同研究・競争的資金等の研究課題

  • マスター方程式によるネットワーク上の感染症ダイナミクスの解析
    科学研究費助成事業 基盤研究(C)
    2016年04月 - 2020年03月
    根本 幸児, 長谷川 雄央
    レギュラーランダムグラフ上でSWIR感染モデルの有限シード(初期感染者)比率からの振る舞いをAME(近似マスター方程式)の数値解析から分析し二つの臨界感染率の存在を明らかにした。また,レギュラーランダムとスケールフリーネットワーク上のSIR感染モデルに隔離対策を導入したモデルを提示し,ランダムワクチン対策に対する優位性を解明した。さらにSISモデルの拡張であるSWIS,SWSIS両モデルを統一的に取り扱い,有限シード比率を変化させて現れる連続相転移と不連続相転移のメカニズムを明らかにした。
    日本学術振興会, 基盤研究(C), 北海道大学, 16K05507
  • 非ユークリッド的グラフにおける確率モデルの多重相転移
    科学研究費助成事業
    2015年04月01日 - 2018年03月31日
    長谷川 雄央, 根本 幸児, 能川 知昭, 岩瀬 優太, 浮田 裕基
    非ユークリッド的グラフ(複雑ネットワーク、nonamenable graph)上に配置された数理モデルは、しばしば(ユークリッド格子系では見られない)新規の相転移を示すことが知られる。本研究では以下のトピックを明らかにし、ネットワークの構造とその上のダイナミクスの関係に関する知見を深めることができた:(1) ボンドパーコレーションにおける臨界相の統計的性質、(2) 階層ネットワーク上のサイトパーコレーションにおける秩序相の消失、(3) コンタクトプロセスが示す非平衡多重相転移の特徴、(4) 感染症モデルダイナミクスにおける初期状態の影響。
    日本学術振興会, 若手研究(B), 茨城大学, 15K17716
  • 細胞組織形成における細胞運動の協同機構の解明
    科学研究費助成事業
    2013年04月01日 - 2018年03月31日
    川端 和重, 水谷 武臣, 根本 幸児
    生体内で細胞集団は、血管のようなパイプ構造や肺胞のような球殻構造など形態を作り出すことによって特定の機能を生み出している。これらの構造は多細胞の協同性のもとに作り出されるが、協調性の起源についてはこれまで明らかにされていない。本研究では、シスト構造を形成する細胞集団をモデル実験細胞として、細胞運動の解析や細胞が出す力の解析法の開発、特定の遺伝子を欠損させた細胞株の樹立、を通じて、協同性の起源に迫った。更には、細胞や細胞外基質の物理パラメータを用いて、シスト構造の形成に対する数値シミュレーションを行った。
    日本学術振興会, 基盤研究(B), 北海道大学, 25287106
  • 細胞コロニー内の細胞に個別に蓄積される力学的記憶の解明
    科学研究費補助金(基盤研究(B))
    2006年 - 2008年
    川端 和重, 芳賀 永, 根本 幸児
    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。
    文部科学省, 基盤研究(B), 北海道大学, 連携研究者, 競争的資金, 18340122
  • ガラス的な系におけるゆらぎに関する統計物理学
    科学研究費補助金(国際学術研究, 基盤研究(B))
    1998年 - 1999年
    高山 一, Bouchaud J.P, Campbell I.A, Orbacn R, 根本 幸児, 西森 秀稔
    本研究計画では、フランス、米国、日本の研究者の間で、また、理論・実験研究者の間で密接な研究交流を計りながら、スピングラスを中心とした'ガラス的な系'における平衡・非平衡ダイナミックスを規定する'ゆらぎ'の本質を解明する研究を進めた。種々の課題に対する個別的な研究を関連メンバーが協力しながら進展させ、それぞれの成果を全体研究集会-Royaumont(仏,10月1998年)、京都(10月1999年)-を開催して全メンバー間で討議し、ガラス的な系におけるゆらぎに共通する普遍的な概念の構築を目指した。以下はその主な研究成果である。1)スピングラス(SG)におけるエイジング現象に関して:a)熱残留磁化の精密測定からSG相関長を抽出し、その成長則を実験的に決定した(Orbach)。b)SGは、温度シフト・サイクルを伴うエイジング過程において一見相矛盾する'若返り効果'と'記憶効果'を示す。これらを位相空間の視点から説明する理論を提起し(Bouchaud)、また、同様の視点から'階層的ランダムエネルギー模型'を提起し、二つの効果の詳細を数値的に検証した(根本)。c)一方、EA模型における同現象に関するシミュレーションを行い、その結果が実スピン空間で構築された液滴描像とよく一致することを明らかにした(高山)。2)SGと不均一な強磁性体・強誘電体とのエイジング現象を比較し、後者はランダムなピン...
    文部科学省, 国際学術研究, 基盤研究(B), 東京大学, 連携研究者, 競争的資金, 10044064
  • コンプレックスな系におけるエイジング現象
    科学研究費補助金(国際学術研究)
    1996年 - 1997年
    高山 一, 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
    要素問の相互作用が互いに競合しているランダム系(コンプレックスな系と呼ぶ)に固有な現象の一つとしてエイジング現象があげられる。種々のスピングラス物質やスピングラス模型における同現象を中心に、超伝導体中の磁束状態など関連分野の問題について理論(シミュレーションを含む)、実験それぞれの研究で得られた個別的な成果によって、コンプレックスな系におけるエイジング現象の基本的なメカニズム、すなわち、位相空間で見た系の自由エネルギー多谷構造に関して、より深い理解に到達した。本研究で得られた具体的成果のうち主なものは以下の通りである。1)スピングラスの階層的な構造を理論的に特徴付けるパリジ重なり分布関数を磁場中エイジング現象から捉える実験に初めて成功し、同関数の定量的な評価を行った(Orbach)。2)クラスタースピングラスとと通常のスピングラスにおけるエイジング現象の間に特徴的な違いのあることを実験的に明らかにした(伊藤)。3)大規模シミュレーションにより、有限サイズのSK模型におけるエイジング過程を統一的に捉える描像を提起した(高山)。4)数値解析により、3次元ハイゼンベルグEA模型のエイジング現象の解析を通して、カイラルグラス転移の存在を強く示唆する結果が初めて得られた(川村)。5)数値解析により、EA模型のスピングラス相転移の臨界特性が相互作用の分布に依存するという非普遍性を見出した...
    文部科学省, 国際学術研究, 東京大学, 連携研究者, 競争的資金, 08044060
  • 双晶面のカオス的運動における数値シュミレーションと精密測定
    科学研究費補助金(基盤研究(B))
    1996年 - 1997年
    川端 和重, 小野寺 彰, 根本 幸児
    有機単結晶(TMTSF)_2Xに発生した孤立した双晶面は一定の応力下で継続運動を行う。この運動様子を精密に測定し、以下の結果を得た。1形態:光学顕微鏡・原子間力顕微鏡および走査型電子顕微鏡の観察により数10nm以下の幅で平面的であり,運動中も光学顕微鏡の精度内で平面的である。2運動全体:一定応力下においても、境界の運動速度は場所によって変化し、場所によっては停止と運動を繰り返すという断続運動を示す。3場所依存性:速度は結晶中の場所ごとに変化する。平均速度で運動の空間依存性は規格化できることから、速度を支配している要因として結晶に固定したピンニングがある。停止と運動は同一運動要因に支配されていると言える。4応力依存性:臨界応力が存在し、臨界応力付近において運動状態にホップ分岐的な断続運動と連続運動の間の移り変わりがある。5待機時間依存性:境界が通過してから再び通過するまでの時間(待機時間)が長くなるほど、同じ応力でも速度は遅くなる。また待機時間を非常に長くした極限では速度は一定値に漸近する。これより、待機時間の間に運動支配する要因に緩和現象が起こっている。結晶内の場所によって待機時間を変えて運動を観測した結果、この緩和は境界自体に起こるのではなく、結晶の各部分で起こっている。6温度依存性:運動速度は温度の上昇に伴って増加する。しかし上昇下降の温度サイクルに対して速度上昇しつづけ...
    文部科学省, 基盤研究(B), 北海道大学, 連携研究者, 競争的資金, 08455048
  • スピングラス系におけるクラスター効果の数値解析
    科学研究費補助金(一般研究(C))
    1994年 - 1995年
    根本 幸児
    スピングラスのようなフラストレーションのあるランダム系で、一般に準安定状態が多数存在すると考えられている。そのような状況の下では多くの場合「ガラス的」な緩和現象が見られると予想され、実験的にも多くの物質で観測されている。異常長緩和現象を説明する理論の背景には、相関の強いスピンクラスターの形成・成長が本質的であるという考えがある。本研究では、クラスターの形成そのものに焦点を絞り、それを空間的な秩序構造の一形態とみなして解析することによって、クラスターの振舞が異常長緩和現象へ果たす役割を解明することを目指したものであった。この目的のため、次のような構成で研究が進められた。1.どのような長緩和現象が発現するかを知るために、短距離相互作用型の±JイジングスピンEdwards-Anderson(EA)模型の高温側における自己相関関数q(t)の性質をモンテカルロシミュレーションによって綿密に調べ、特に対応する強磁性模型の転移温度以下におけるGriffith相にどのように移行するかが解明された。2.異常長緩和現象は、モンテカルロシミュレーションを行なう上で、大きな障害となる。殊に、低温側では熱平衡に至る時間が計算実行可能時間を大幅に上回り、事実上実行不可能であった。この困難を克服するため、我々がレプリカ交換法と呼ぶ新しいシミュレーションの方法を開発し、その有効性が確かめられた。3.上記の方...
    文部科学省, 一般研究(C), 北海道大学, 研究代表者, 競争的資金, 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年 - 1994年
    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, 連携研究者, 競争的資金, 06640493
  • 現実の物質におけるエルゴ-ド・非エルゴ-ド的転移現象
    科学研究費補助金(一般研究(C))
    1989年 - 1990年
    高山 一, 根本 幸児
    スピングラスの位相空間における自由エネルギ-構造は、高温で単純な一谷構造のものが、低温では複雑な多谷構造をとる。谷間の障壁が着目する温度に比べて十分高いと、系は谷間を移動できなくなり、非エルゴ-ド的であると見なされる。このようなエルゴ-ド・非エルゴ-ド的転移現象はスピングラスの平均場理論によって初めて具体的に定式化された。現実の様々な物質で見られる類似の現象を理解するためには、出発点となる平均場模型に関する十分な理解が必要であると考え、数値的な取扱いが比較的容易な、ナイ-ブ平均場模型を詳しく解析し、以下の結果を得た。(1)この模型とSK模型とをつなげる一連の平均場模型群を提案し、それらが多数の準安定状態をもつこと、スピングラス相のマ-ジナル安定性などを明らかにした。(2)ナイ-ブ平均場模型について、有限サイズのサンプルにおける全ての準安定状態を探し尽す数値的解析から、準安定状態の位相空間における分布(準安定状態間の磁化の重なりの分布で指定される)が、レプリカ法から導びかれた普遍的に分布則に従うことを初めて具体的に検証した。この普遍的に分布則が有限な磁場中でも成立することも明らかにした。(3)ランダムな相互作用の平均値が大きく、リエントラント転移が出現する系について、この転移に伴う準安定状態の位相空間における分布の特徴を解析した。現実のスピングラスにより近い、短距離型相互作用の...
    文部科学省, 一般研究(C), 筑波大学, 連携研究者, 競争的資金, 01540298
  • 専用機によるイジング系の研究
    科学研究費補助金(総合研究(A))
    1988年 - 1990年
    鈴木 増雄, 根本 幸児, 宮下 精二, 香取 真理, 桂 重俊
    従来、専用計算機は製作グル-プの手元に一台だけあるという状況であった。我々の開発したイジングモデル専用計算機mーTIS(mーTISIIのベ-スとなったマシ-ン)もそうであった。本研究プロジェクトの最大の目的は、専用計算機を関連分野の研究者がだれでも使用でき、それによりイジングモデル周辺の基礎理論の進歩を促がすことであった。本研究プロジェクトではこのイジングマシ-ンを13台製作し、このことによって目的は達成された。進後はmーTISIIを活用して共同研究者とともに様々な問題を究明するために活用してゆく予定である。当初の計画では回路のLSI化、ボ-ドの製作をすべて外注によって賄う予定であった。しかし、予算の都合上、この計画のように遂行することが不可能となった。このため、LSIとしてLCAを採用し、シリコンチップ上に乗せる作業まで全て研究室で行った。このためマシ-ン開発に予定以上の労力を要したが、研究プロジェクト終了までに完成でき、日本各地の共同研究者のもとへ配備を完了することができた。また理論研究用の専用計算機において、「ハ-ドウエアのソフト化」という設計上の自由度がどのようにすれば有効な手段となるのかも、本研究によりあきらかとなった。これらのハ-ドウエア上の成果の他に、本研究プロジェクトの一環として開催した研究会等を通して、専用計算機をどのように活用してゆくかという(研究体制もふ...
    文部科学省, 総合研究(A), 東京大学, 連携研究者, 競争的資金, 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年 - 1988年
    根本 幸児
    日本学術振興会, 奨励研究(A), 東京大学, 63790178

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