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

随着凝聚态物理研究的不断深入，计算机模拟的作用也越来越大。动态缓慢的问题往往使模拟变得困难。为了解决这个问题，计算物理领域迫切需要解决这个问题。本研究的目的是提出新的模拟算法，并将其应用于复杂的随机和/或量子自旋系统，这些系统一直被认为是难以解决的。我处理了二维XY模型和离散时钟模型。我证明了KT转变点随着稀释在逾渗阈值处平滑地变为零。在时钟模型的情况下，存在第二个低温KT跃迁，并且该跃迁的跃迁点在渗流阈值处也变为零。我还证明了临界指数η是一个普适量，也就是说， ...更多信息 这取决于稀释的程度。此外，我还将研究扩展到q态Villain模型，在此模型中，对偶关系成立，并基于对偶关系考察了临界指数之间的关系。其次，提出了一种新的非等重模拟方法。平衡系统的重新加权方法已经得到了很好的建立，其中通过对玻尔兹曼因子进行重新加权，从某个温度下的模拟中计算不同温度下的物理量。我把这种重新加权的方法推广到依赖于时间的非平衡系统。利用统计学中的序贯重要抽样方法，提出了非平衡态重赋权方法，并将其应用于Ising模型的非平衡态松弛分析。此外，我应用非平衡重加权方法的驱动扩散格子气模型，它显示了非平衡相变，并表明，可以确定临界温度和估计的动力学指数z准确地与较少的计算工作量。第三，讨论了Langevin型方程与磁系统动力学的Monte Carlo方法之间的关系。我想到了纳米磁铁的应用。得到了将蒙特卡罗方法中出现的“时间”与真实的时间结合的联合收割机因子。我证明了这种方法对单个粒子和磁体组装的有效性。少

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