Monte Carlo Simulation of Quantum and Random Spin Systems

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The effect of randomness on phase transitions and critical phenomena is an interesting problem. The purpose of the present study is to perform massive Monte Carlo simulation for getting accurate numerical information on quantum and random spin systems. We here focus on three topics from several subjects.First, we have studied the problem of the universal finite-size scaling. We have shown that this concept can be applied to the two-dimensional Ising model, where we have paid special attention to the boundary conditions. Especially, we have studied the finite-size scaling of the rectangular lattice with tilted boundary conditions.Second, we have applied the exchange Monte Carlo method to the ordering dynamics of the three-component system with the conserved order parameter. We have observed a rapid domain growth even for the deeply quenched case to low temperatures, and have found that a domain growth is controlled by a simple algebraic growth law with the exponent 1/3.Third, we have developed a new fast simulation method to study phase separation under shear flow by using spin model. It enables us to study the effect of thermal fluctuation on phase separation which could not be studied by conventional simulation methods. We have also proposed a new method to analyze anisotropic temporal evolution of structure factor.