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

计算机仿真的作用随着凝聚态物理学的研究的进展而发展。缓慢动态的问题通常会使模拟变得困难。在计算物理领域急需解决这个问题，该研究项目的目的是提出新的仿真算法，以将它们应用于复杂的随机和/或量子旋转系统，这些系统被认为难以解决。我处理了二维XY模型和离散时钟模型。我表明，在渗透阈值下，KT过渡点在渗透阈值下平稳地变为零。在时钟模型的情况下，有第二个低温KT转变，并且该过渡的过渡点在渗透阈值下也变为零。我还表明，临界指数η是通用数量，也就是说，指数确实……更多取决于稀释程度。此外，我将研究扩展到了Q-State的反派模型，在该模型中，确切的二元关系存在，并根据双重性研究了关键指数之间的关系。其次，我开发了一种新的仿真方法，用于非平衡重新加权。平衡系统的重新加权方法是，通过在某个温度下的模拟中，通过玻尔茨曼因子重新权在不同温度下计算物理量，可以很好地确定。我将这种重新加权技术扩展到取决于时间的非平衡系统。使用在统计领域中使用的顺序重要性采样方法，我制定了非平衡重新加权的方法，并将其应用于Ising模型的非平衡弛豫分析。此外，我将非平衡重新加权方法应用于驱动的不同晶格气模型，该模型显示了非平衡相变的型号，并表明人们可以通过较少的计算工作来确定临界温度并准确地估算动态指数。第三，我讨论了langevin型方程与磁系统动力学的蒙特卡洛方法之间的关系。我将应用于纳米磁铁的应用。我获得了将蒙特卡洛法中出现的“时间”与实时相结合的因素。我在单个粒子和磁体组装中都展示了该方法的有效性。较少的

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.

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：

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.

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.