K. Hukushima

The University of Tokyo, Department of Basic Science, Faculty Member

Followers

Following

Co-authors

Public Views

Interests

Uploads

Papers by K. Hukushima

Population Annealing and Its Application to a Spin Glass

AIP Conference Proceedings, 2003

A way to modify simulated annealing to a Monte Carlo algorithm for calculating canonical averages... more A way to modify simulated annealing to a Monte Carlo algorithm for calculating canonical averages is presented. The proposed algorithm is based on the idea of population based Monte Carlo method where multiple replicas of the original system are used to represent a target distribution. Inspired by non-equilibrium work relation of Jarzynski, an appropriate weight of the replicas is introduced,

Dynamical aspects of a three-dimensional Heisenberg spin glass

Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are ... more Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are studied both by equilibrium and off-equilibrium Monte Carlo simulations with emphasis on their dynamical aspects. The model is found to exhibit a finite-temperature chiral-glass transition without the conventional spin-glass order. Although chirality is an Ising-like quantity from symmetry, universality class of the chiral-glass transition appears to be different

Download

Chiral-glass and replica symmetry breaking of a three-dimensional Heisenberg spin glass

Dynamical critical phenomena in three-dimensional Heisenberg spin glasses

Physical Review B, 2002

Evidence of a one-step replica symmetry breaking in a three-dimensional Potts glass model

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We study a seven-state Potts glass model in three dimensions with first-, second-, and third-near... more We study a seven-state Potts glass model in three dimensions with first-, second-, and third-nearest-neighbor interactions with a bimodal distribution of couplings by Monte Carlo simulations. Our results show the existence of a spin-glass transition at a finite temperature T_{c}, a discontinuous jump of an order parameter at T_{c} without latent heat, and a nontrivial structure in the order parameter distribution below T_{c}. They are compatible with one-step replica symmetry breaking.

Download

Minimum vertex cover problems on random hypergraphs: replica symmetric solution and a leaf removal algorithm

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

The minimum vertex-cover problems on random α-uniform hypergraphs are studied using two different... more The minimum vertex-cover problems on random α-uniform hypergraphs are studied using two different approaches, a replica method in statistical mechanics of random systems and a leaf removal algorithm. It is found that there exists a phase transition at the critical average degree e/(α-1), below which a replica symmetric ansatz in the replica method holds and the algorithm estimates exactly the same solution of the problem as that by the replica method. In contrast, above the critical degree, the replica symmetric solution becomes unstable and the leaf-removal algorithm fails to estimate the optimal solution because of the emergence of a large size core. These results strongly suggest a close relation between the replica symmetry and the performance of an approximation algorithm. Critical properties of the core percolation are also examined numerically by a finite-size scaling.

Download

Domain-wall free energy of spin-glass models: numerical method and boundary conditions

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999

An efficient Monte Carlo method is extended to evaluate directly domain-wall free energy for rand... more An efficient Monte Carlo method is extended to evaluate directly domain-wall free energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition are investigated in the 4d+/-J Ising model under the replica boundary condition. Our values of the critical temperature and exponent, obtained by finite-size scaling, are in good agreement with those of the standard Monte Carlo and the series expansion studies. In addition, two exponents, the stiffness exponent and the fractal dimension of the domain wall, which characterize the ordered phase, are obtained. The latter value is larger than d-1, indicating that the domain wall is really rough in the 4d Ising spin-glass phase.

Download

Replica-symmetry-breaking transition in finite-size simulations

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

Finite-size effects in the mean-field Ising spin glass and the mean-field three-state Potts glass... more Finite-size effects in the mean-field Ising spin glass and the mean-field three-state Potts glass are investigated by Monte Carlo simulations. In the thermodynamic limit, each model is known to exhibit a continuous phase transition into the ordered state with a full and a one-step replica-symmetry breaking (RSB), respectively. In the Ising case, the Binder parameter g calculated for various finite sizes remains positive at any temperature and crosses at the transition point, while in the Potts case g develops a negative dip without showing a crossing in the g>0 region. By contrast, non-self-averaging parameters always remain positive and show a clear crossing at the transition temperature in both cases. Our finding suggests that care should be taken in interpreting the numerical data of the Binder parameter, particularly when the system exhibits a one-step-like RSB.

Chiral-glass transition and replica symmetry breaking of a three-dimensional heisenberg spin glass

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg sp... more Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a finite-temperature chiral-glass transition without the conventional spin-glass order is established. Critical exponents characterizing the transition are different from those of the standard Ising spin glass. The calculated overlap distribution suggests the appearance of a peculiar type of replica-symmetry breaking in the chiral-glass ordered state.

Download

Monte Carlo Simulation on Aging Phenomena in the SK Spin-Glass Model: Temperature Dependence of the Time Evolution of Energy

Springer Proceedings in Physics, 1998

Domain-Wall Renormalization-Group Study of Spin-Glass Models

Condensed Matter: Electronic Properties, etc.-Aging of the Zero-Field-Cooled Magnetization in Ising Spin Glasses: Experiment and Numerical Simulation

Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties-Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model: III. Cumulative Memory and'Chaos' Effects in

Equilibrium Study of Spin-Glass Models: Monte Carlo Simulation and Multi-variate Analysis

LETTERS-Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties-Field-Shift Aging Protocol on 3D Ising Spin-Glass Model: Dynamical Crossover between the Spin-Glass and

Statistical physics of disordered systems and its applications-Preface

2F1412 統計力学的進化模型における表現型揺らぎの効果とレプリカ対称性 (数理生物学 2, 第 49 回日本生物物理学会年会)

Numerical Detection of the Ergodicity Breaking in a Lattice Glass Model

We directly detect the ergodicity breaking in a lattice glass model by a numerical simulation. Th... more We directly detect the ergodicity breaking in a lattice glass model by a numerical simulation. The obtained results nicely agree with those by the cavity method that the model on a regular random graph exhibits a dynamical transition with the ergodicity breaking at an occupation density. The present method invented for a numerical detection of the ergodicity breaking is applicable to glassy systems in finite dimensions.

Download

Computational experiment on glassy dynamic nature of field-cooled magnetization in Ising spin-glass model

The field-cooled (FC) process on an Ising spin-glass model is investigated by a standard Monte Ca... more The field-cooled (FC) process on an Ising spin-glass model is investigated by a standard Monte Calro (MC) method on one hand, and the equilibrium magnetization of the same system is evaluated by the exchang MC method on the other hand. The two types of simulation reveal intriguing glassy (nonequilibrium) dynamic properties of the FC magnetization (FCM) of the system. Particularly, the FCM decrease is observed when the FC process is halted at a low temperater, although its value is smaller than the corresponding equilibrium value. We present a comprehensive interpretation of such peculiar phenomena based on the scenario for the FCM process recently propsed by Jönsson and one of us (HT).

Download

Identification of metastable states in finite temperature simulations: A self-organization approach

K. Hukushima

Uploads

Papers by K. Hukushima

Log In