International Journal of Modern Physics C

The purpose of the present paper is to review briefly the quantum analysis and to apply it in deriving quantum correlation identities. These give the nonlinear response of isotropic magnetic systems in the presence of a finite magnetic field. Hybrid exponential product formulas are also discussed from the point of computationics, as an application of the quantum analysis.

This paper discusses how slow dynamics can occur in the vicinity of quantum phase transitions. In addition to critical slowing down, there are two additional sources of slow dynamics. Firstly, even for a pure system, there is a phase coherence time which diverges as the temperature tends to zero. This is hard to see from numerical studies in imaginary time and real time dynamics are needed. Secondly, in random systems, Griffiths–McCoy singularities occur at low temperature because of rare regions which are "locally in the wrong phase" due to of statistical fluctuations in the random interactions. These are particularly strong for systems with discrete, e.g., Ising, symmetry. The form of Griffiths–McCoy singularities in real time is not understood.

Ground-state phase transition of site-diluted Heisenberg antiferromagnets on a square lattice is studied. By using the continuous-time loop algorithm, we perform large-scale quantum Monte Carlo simulation on large systems at quite low temperatures. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the classical percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. It is found that the transition is not universal, i.e., the critical exponents depend on the spin size S.

This paper deals with the optimization of trial states for the computation of dominant eigenvalues of operators and very large matrices. In addition to preliminary results for the energy spectrum of van der Waals clusters, we review results of the application of this method to the computation of relaxation times of independent relaxation modes at the Ising critical point in two dimensions.

An investigation for numerical method to study quantum dynamics in dissipative environments is presented, studying the resonant tunneling phenomena of the low temperature magnetization process of Mn₁₂. It is pointed out that information of pure quantum transition can be obtained from deceptive nonadiabatic transitions due to the dissipative environments.

Efficient cluster algorithms for Ising systems with fields are described. Cluster are grown between two replicas of the system in the same field. As is the case for other successful cluster approaches, the critical point of the spin system coincides with the percolation threshold of the clusters. Applications are discussed.

Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. The simulation results not only in isothermal aging but also in T-shift aging process. T-shift aging processes exhibit the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls in spite of the fact that the growth law for these length scales still shows a pre-asymptotic behavior compared with the asymptotic form proposed by the droplet theory. Implications of our simulational results are also discussed in relation to experimental observations.

We investigate a binary Lennard–Jones mixture with molecular dynamics simulations. We consider first a system cooled linearly in time with the cooling rate γ. By varying γ over almost four decades we study the influence of the cooling rate on the glass transition and on the resulting glass. We find for all investigated quantities a cooling rate dependence; with decreasing cooling rate the system falls out of equilibrium at decreasing temperatures, reaches lower enthalpies and obtains increasing local order. Next we study the dynamics of the melting process by investigating the most immobile and most mobile particles in the glass. We find that their spatial distribution is heterogeneous and that the immobile/mobile particles are surrounded by denser/less dense cages than an average particle.

A heuristic optimization algorithm is developed based on the renormalization group idea and applied to the Edwards–Anderson model in two dimensions with symmetric Gaussian bond distribution. Droplets are forced to excite by the boundary condition. We find that the droplets have nontrivial fractal dimension not only for its surface but also for its volume, in contrast to what has been implicitly assumed in conventional droplet arguments.

We describe a Monte Carlo simulation study of the magnetic phase diagram of diluted magnetic semiconductors doped with shallow impurities in the low concentration regime. We show that because of a wide distribution of interaction strengths, the system exhibits strong quantum effects in the magnetically ordered phase. A discrete spin model, found to closely approximate the quantum system, shows long relaxation times, and the need for specialized cluster algorithms for updating spin configurations. Results for a representative system are presented.

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 from that of the standard Ising spin glass. In the off-equilibrium simulation, while the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observered in the mean-field model.

An overview of advanced dynamical algorithms capable of spanning the widely disparate time scales that govern the decay of metastable phases in discrete spin models is presented. The algorithms discussed include constrained transfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), and projective dynamics (PD) methods. The strengths and weaknesses of each of these algorithms are discussed, with particular emphasis on identifying the parameter regimes (system size, temperature, and field) in which each algorithm works best.

Nonequilibrium relaxation (NER) process turns out to be an useful method to study phase transition and critical phenomena. The NER method and its applications are reviewed. Characteristic behavior of the local exponent is analyzed with a simple model.

The Projected Dynamics method was originally developed to study metastable decay in ferromagnetic discrete spin models. Here, we apply it to a classical, continuous Heisenberg model with anisotropic ferromagnetic interactions, which evolves under a Monte Carlo dynamic. The anisotropy is sufficiently large to allow comparison with the Ising model. We describe the Projected Dynamics method and how to apply it to this continuous-spin system. We also discuss how to extract metastable lifetimes and how to extrapolate from small systems to larger systems.

We report the application of the Monte Carlo simulation to phase separation dynamics. First, we deal with the phase separation under shear flow. The thermal effect on the phase separation is discussed, and the anisotropic growth exponents in the late stage are estimated. Next, we study the effect of surfactants on the three-component solvents. We obtain the mixture of macrophase separation and microphase separation, and investigate the dynamics of both phase separations.

For many years the emphasis in protein-folding simulations has been laid as to how to predict the three-dimensional structure of proteins. Only recently has there be a shift in interest towards the thermodynamics of folding. We show that generalized-ensemble techniques are well suited to study both questions for realistic protein models.

Slow dynamics of complex domain structures in phase separating polymer systems is investigated with the use of the self-consistent field (SCF) dynamic density functional (DDF) technique where the free energy of the system is calculated using the path integral formalism of the polymer chain conformation. We apply this technique to micellization of block copolymers and to phase separation of polymer blends containing block copolymers as a compatibilizer. In order to study the late stage of the phase separation processes more efficiently, we adopt the so-called Ginzburg–Landau approach, where a phenomenological model free energy functional is used. Numerical results of this approach is quantitatively compared with the results of the SCF approach.

Using Suzuki–Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special cases, also conserve the energy and maintain time reversibility. We investigate integration schemes of up to eighth order and show that these new algorithms can be used with much larger time steps than a well established predictor–corrector method. These methods may lead to a substantial speedup of spin dynamics simulations, however, the choice of which order method to use is not always straightforward.

The local mobility of particles in highly supercooled liquids is demonstrated to be spatially heterogeneous on time scales comparable to the structural relaxation time τ_α. The particle motions in the active regions dominantly contribute to the mean square displacement, giving rise to a diffusion constant systematically larger than the Stokes–Einstein value. The diffusion process eventually becomes homogeneous on time scales longer than the life time of the heterogeneity structure (~ 3τ_α). The heterogeneity structure in the local mobility is very analogous to the critical fluctuation in Ising spin systems with their structure factor being excellently fitted to the Ornstein–Zernike form.

Although histogram methods have been extremely effective for analyzing data from Monte Carlo simulations, they do have certain limitations, including the range over which they are valid and the difficulties of combining data from independent simulations. In this paper, we describe a complementary approach to extracting information from Monte Carlo simulations that uses the matrix of transition probabilities. Combining the Transition Matrix with an N-fold way simulation technique produces an extremely flexible and efficient approach to rather general Monte Carlo simulations.

Monte Carlo simulations based on simulated annealing and multicanonical algorithm have been performed to predict the secondary and tertiary structures of oligopeptide systems. Two oligopeptides, C-peptide of ribonuclease A and the fragment BPTI(16-36) of bovine pancreatic trypsin inhibitor, were studied. Only the amino-acid sequence information was used as input and initial conformations were randomly generated. The lowest-energy conformations obtained have α-helix structure and β-sheet structure for C-peptide and BPTI(16-36), respectively, in remarkable agreement with experimental results.