Monte Carlo Studies of Random Spin Systems with Complex Structures

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Effects of randomness on phase transitions and critical phenomena are interesting subjects of study. The purpose of the present research project is to investigate random spin systems by using Monte Carlo simulations. We have studied the relation between the phase transition of spin systems and geometric percolation transition, the finite-size scaling (FSS) of spin systems with anisotropic shape, and the phase separation dynamics of complex systems.First, based on the connection between the phase transition of the Ising model and the geometric percolation problem, we have studied the importance of the multiple percolating clusters for anisotropic Ising models. We have applied this idea to the random diluted Ising model, and discussed the crossover from the percolation fixed point to the thermal fixed point.Second, we have investigated the FSS functions for anisotropic Ising models. The anisotropic parameter dependence of FSS functions has been studied. For the anisotropic three-dimensional Ising models, we have obtained a unified view of three-dimensional and two-dimensional FSS, from the analysis of the FSS near the critical temperature of the layered Ising model.Third, we have investigated the phase separation dynamics under shear flow. Developing a new Monte Carlo method to study the phase separation under shear flow based on the spin model of the Kawasaki dynamics, we have discussed the anisotropic growth exponents in the late stage.