Nobuyasu Ito

Nonequilibrium relaxation method

The nonequilibrium relaxation (NER) method is a numerical technique to analyse equilibrium phase transitions. One can estimate the transition point and critical exponents calculating relaxations of order parameter and fluctuations in NER processes from nonequilibrium initial states to the equilibrium ones. It is applied to the second-order transition as well as the first-order one; the precise estimation of transition temperature for the latter case is achieved with the mixed phase initialization technique. Since the equilibration is not necessary in the simulation, one can analyse systems with large sizes which can be recognized as in the thermodynamic limit up to the observation time. This leads to the analysis being more efficient for slowly relaxing systems with frustrations and randomness. It can be extended to the Kosterlitz?Thouless transition and the spin glass transition cases by the use of the finite-time scaling analysis. It is also extended to quantum systems.

Nonequilibrium relaxation study on spin glass model

Ferromagnetic (FM) transition point and universality class of the ±J Ising model on cubic lattice are studied by computer simulation using the nonequilibrium relaxation (NER) method. At FM bond density p between multicritical one pmc and 1, static exponents take universal values which are different from those of p=1 or p=pmc, and they are consistent with the values of the random-fixed point and of the simulations and experiments for diluted Ising systems. The dynamical exponent, however, seems to depend on p and not to be universal, although it may be due to finite-time correction. The estimation of pmc on square lattice is also refined to be 0.8894(9), which is consistent with the Nishimori and Nemotos conjecture, 0.889972⋯.

Nonequilibrium relaxation method : An alternative simulation strategy

One well-established simulation strategy to study the thermal phases and transitions of a given microscopic model system is the so-called equilibrium method, in which one first realizes the equilibrium ensemble of a finite system and then extrapolates the results to infinite system. This equilibrium method traces over the standard theory of the thermal statistical mechanics, and over the idea of the thermodynamic limit. Recently, an alternative simulation strategy has been developed, which analyzes the nonequilibrium relaxation (NER) process. It is called theNER method. NER method has some advantages over the equilibrium method. The NER method provides a simpler analyzing procedure. This implies less systematic error which is inevitable in the simulation and provides efficient resource usage. The NER method easily treats not only the thermodynamic limit but also other limits, for example, non-Gibbsian nonequilibrium steady states. So the NER method is also relevant for new fields of the statistical physics. Application of the NER method have been expanding to various problems: from basic first- and second-order transitions to advanced and exotic phases like chiral, KT spin-glass and quantum phases. These studies have provided, not only better estimations of transition point and exponents, but also qualitative developments. For example, the universality class of a random system, the nature of the two-dimensional melting and the scaling behavior of spin-glass aging phenomena have been clarified.

Recent Development in Nonequilibrium Relaxation Method

Recent results of the simulational studies on phase transition using nonequilibrium(or off-equilibrium) relaxation (NER) functions are reviewed. The values of transition point and the exponents are estimated for Ising model on cubic lattice. Universalities of the classical XY and Heisenberg models, and clock and polyhedral models are also studied. A NER method to identify the first-order transition is given. For Kosterlitz-Thouless (KT) transition, scaling analysis of NER function works to evaluates the transition point and the exponents. An evidence of KT transition in two-dimensional melting phenomena is included.

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and this relationship is confirmed for our method by observing nonequilibrium relaxation of a bond-orientational order parameter. The rejection-free method gives a greater computational efficiency than the standard method at high densities. The rejection free method is implemented in a shrewd manner using optimization methods to calculate a rejection probability and to update the system. This method should allow an efficient study of the dynamics of two-dimensional solids at high density.We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to exp(constbeta) in the Ising, sqrt[beta] in the classical XY, and beta in the classical Heisenberg spin systems with inverse temperature beta, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to (rho(cp)-rho)(-d) with the closest packing density rho(cp), density rho, and dimension d of the systems. We construct and implement a rejection-free Monte Carlo method for the hard-disk system. The RFMC has a greater computational efficiency at high densities, and the density dependence of the efficiency is as predicted by our arguments.

Positional order and diffusion processes in particle systems

The relaxation of a nonequilibrium solid to a fluid is determined by observing the positional order parameter in Monte Carlo simulations, and discussed based on diffusion processes in the hard-particle systems. From the cumulant expansion up to the second order, the relation between the positional order parameter Psi and the mean square displacement is obtained to be Psi approximately exp(-K2/2d) with a reciprocal vector K and the dimension of the system d. On the basis of this relation, the positional order should decay exponentially as Psi is approximately exp(-K2Dt) when the system involves normal diffusion with a diffusion constant D. A diffusion process with swapping positions of particles is also discussed. The swapping of particles contributes to the higher orders of the cumulants, and swapping positions allows particles to diffuse without destroying the positional order while the normal diffusion destroys it.

Rate Constant in Far-from-Equilibrium States of a Replicating System with Mutually Catalyzing Chemicals

As a first step to study reaction dynamics in far-from-equilibrium open systems, we propose a stochastic protocell model in which two mutually catalyzing chemicals are replicating depending on the external flow of energy resources J. This model exhibits an Arrhenius type reaction; furthermore, it produces a non-Arrhenius reaction that exhibits a power-law reaction rate with regard to the activation energy. These dependences are explained using the dynamics of J; the asymmetric random walk of J results in the Arrhenius equation and conservation of J results in a power-law dependence. Further, we find that the discreteness of molecules results in the power change. Effects of cell divisions are also discussed in our model.

Nonequilibrium Relaxation Study on the Ferromagnetic Transition of Ising Spin Glass Model

Ferromagnetic transition of the ±J Ising model is studied simulationally for the cubic lattice. Nonequilibrium relaxation method is used to locate the transition point and to estimate the values of exponents. The dynamical exponent z increases smoothly when the density of ferromagnetic interaction, p, is decreased from 1. The static exponents are changed discontinuously when p is decreased from 1, and they stay in a universality class when p mc < p < 1, where p mc denotes the value of multicritical density. At p = p mc, the static exponents are different from those in p mc < p < 1 and p = 1

Nonequilibrium Relaxation Analysis of Frustrated XY Models in Two Dimensions

We apply the nonequilibrium relaxation (NER) method to the fully- frustrated XY models on square and triangular lattices, in which the possibility of two different transitions, the chiral transition and the Kosterlitz-Thouless one, have been discussed. Further, we calculate the NER functions of fluctuations for these models, and analyze the universality class of them

Dynamical Rushbrooke's inequality for nonequilibrium relaxation process

An inequality for dynamic critical exponents is proved for relaxation processes of arbitrary magnetic systems. This is a dynamical extension of Rushbrookes inequality. It can be applied to any continuous-transition systems with various dynamics. The relation is demonstrated on the result of nonequilibrium relaxation analysis of fluctuations applied to the three-dimensional ferromagnetic Ising model.