Research of random and quantum spin systems using newly developed Monte Carlo algorithms

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The role of computer simulations has been grown with the progress in the research of condensed matter physics. The problem of slow dynamics often makes simulations difficult. To conquer this problem is urgently needed in the field of computational physics The purpose of this research project is to propose new simulation algorithms together with to apply them to complex random and/or quantum spin systems which have been regarded as difficult to solve.First, I studied the dilution effects on the systems which show the Kosterlitz-Thouless (KT) transition. I treated the two-dimensional XY model and the discrete clock model. I showed that the KT transition point becomes zero smoothly at the percolation threshold with dilution. In the case of the clock model there is a second low-temperature KT transition, and the transition point of this transition also becomes zero at the percolation threshold. I also showed that the critical exponent η is a universal quantity, that is, the exponent does n … More ot depend on the degree of dilution. Moreover, I extended the study to the q-state Villain model where the exact duality relation holds, and examined the relation between the critical exponents based on the duality. Second, I developed a new simulation method for the nonequiibrium reweighting. The reweighting method for the equilibrium systems, where from a simulation at some temperature one calculates the physical quantity at a different temperature with the reweighting of the Boltzmann factor, is well established. I extended this reweighting technique to the nonequiibrium systems which depend on time. Using the sequential importance sampling method which is used in the field of statistics, I formulated the method of nonequilibrium reweighting, and applied it to the analysis of nonequilibrium relaxation of the Ising model. Moreover, I applied the nonequilibrium reweighting method to a driven diffusive lattice gas model, which shows the nonequilibrium phase transition, and showed that one can determine the critical temperature and estimate the dynamical exponent z accurately with less computational effort. Third, I discussed the relation between the Langevin-type equation and the Monte Carlo method for the dynamics of magnetic systems. I have the application to the nano magnets in mind. I obtained the factor to combine the "time" which appears in the Monte Carlo method with the real time. I showed the effectiveness of this method both for the single particle and the assembly of magnets. Less