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

使用新开发的蒙特卡罗算法研究随机和量子自旋系统

基本信息

批准号：
15540374
负责人：
OKABE Yutaka
金额：
$ 2.05万
依托单位：
TOKYO METROPOLITAN UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

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

随着凝聚态物理研究的不断深入，计算机模拟的作用越来越大。缓慢的动力学问题常常使模拟变得困难。为了克服这一问题是计算物理领域迫切需要的。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。首先，我研究了呈现Kosterlitz-Thouless(KT)相变的系统的稀释效应。我处理了二维XY模型和离散时钟模型。我证明了随着稀释，KT转变点在渗流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转变，并且该转变的转变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，也就是指数n…更多的是取决于稀释的程度。此外，我还将研究推广到确切对偶关系成立的Q态小人模型，并考察了基于对偶关系的临界指数之间的关系。其次，提出了一种新的非平衡加权的仿真方法。平衡体系的重加权方法是建立的，其中通过在某一温度下的模拟，通过重新加权玻尔兹曼因子来计算在不同温度下的物理量。我将这种重新加权技术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性抽样方法，建立了非平衡重权方法，并将其应用于伊辛模型的非平衡松弛分析。此外，我将非平衡加权方法应用于一个驱动扩散格子气体模型，该模型显示了非平衡相变，并表明可以用较少的计算量准确地确定临界温度和估计动力学指数z。第三，讨论了磁性系统动力学的朗之万型方程和蒙特卡罗方法之间的关系。我已经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”与实时相结合的因子。我展示了这种方法在单个粒子和磁体组装方面的有效性。较少

项目成果

期刊论文数量（109）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Novel Monte Carlo algorihms and their applications

新颖的蒙特卡罗算法及其应用

DOI：
发表时间：
2003
期刊：
Physica A 321・1-2
影响因子：
0
作者：
J.-S.Wang;et al.;Y.Okabe et al.
通讯作者：
Y.Okabe et al.

Novel Monte Carlo algorithms and their applications

新颖的蒙特卡罗算法及其应用

DOI：
发表时间：
2003
期刊：
Physica A 321
影响因子：
0
作者：
J.-S.Wang;et al.;Y.Okabe et al.
通讯作者：
Y.Okabe et al.

Y.Maniwa et al.: "A one-dimensional Ising model for C_<70> molecular ordering in C_<70>-peapods"New J.Phys.. 5. 127-1-127-5 (2003)

Y.Maniwa 等人：“C_<70>-peapods 中 C_<70> 分子排序的一维 Ising 模型”New J.Phys.. 5. 127-1-127-5 (2003)

DOI：
发表时间：
期刊：
影响因子：
0
作者：
通讯作者：

Field-induced Berezinskii-Kosterlitz-Thouless Transition and String-Density Plateau in Anisotropic Triangular Antiferromagnetic Ising Model

各向异性三角反铁磁伊辛模型中场诱导的别列津斯基-科斯特利茨-托勒斯转变和弦密度平台

DOI：
发表时间：
2006
期刊：
Phys. Rev. E 73
影响因子：
0
作者：
X.Cheng et al.;H.Otsuka et al.
通讯作者：
H.Otsuka et al.

Study of the fully frustrated clock model using the Wang-Landau algorithm

基于Wang-Landau算法的完全挫败时钟模型研究

DOI：
发表时间：
2004
期刊：
J.Phys.A 37
影响因子：
0
作者：
T.Surungan;Y.Okabe;H.Otsuka et al.;H.K.Lee et al.;T.Surungan et al.;C.Yamaguchi et al.;H.Otsuka et al.;M.Iwamatsu et al.;Y.Maniwa et al.;T.Surungan et al.
通讯作者：
T.Surungan et al.