短时动力学方法及应用

论文编号:WLX112  字数:8482,页数:19

摘    要
 相变和临界现象是系统由一种稳定状态向另一种稳定状态的突变过程，是统计物理和凝聚态物理的重要研究对象。近年来，随着计算机技术的发展，数值模拟已成为研究相变与临界现象的一种重要的方法。本文采用短时动力学方法模拟处于临界相变下的二维Ising 模型的自旋。
 首先从理论上讨论了Monte Carlo方法和数值模拟方法，引入了重要抽样、细致平衡条件、 Metropolis 算法和Heat-bath算法等。然后从理论上阐述了各类自旋模型及其平衡态和非平衡态，引入了临界慢化、cluster算法、Ising模型等。在此基础上，我们用Monte Carlo方法模拟了二维 Ising 模型相变，得到了随时间的演化规律且进行了相关讨论。
关键词： 短时动力学  临界慢化  Monte Carlo方法  Ising模型

Abstract
 The system proceed which breaks from one steady state to another is called phase transitions and critical phenomena. They’re significant study objects of statistical physics and condensed state physics. In recent years, with the development of computer technology, it already made numerical simulations become an effective method in studying transitions and critical phenomena. The present paper adopts short-time dynamics method to simulate spin of tow-dimension Ising model in the critical phase transition.
 Firstly, we discussed the Monte Carlo method and numerical simulation method theoretically, and introduced importance sampling, detailed balancing condition, Metropolis algorithm and Heat-bath algorithm etc. Then we illustrated all kinds of spin model along with their equilibrium states and nonequilibrium states theoretically, and introduced critical slowing, cluster algorithm and Ising model etc. On this basic, with Monte Carlo method, we simulated phase transition of tow-dimension Ising model. We came to a conclusion of law evolved by time and conducted relevant discussions.
Keywords: short-time dynamics   critical slowing   Monte Carlo method   Ising model

目  录
中文摘要 i
英文摘要 ii
目录 iii
第一章     绪论  1
第二章     Monte Carlo方法  2
 2.1  Monte Carlo随机抽样基本方法 2
2.1.1  简单抽样的Monte Carlo方法 2
2.1.2  重要抽样的Monte Carlo方法 2
 2.2  Metropolis算法 2
 2.3  Heat-bath算法 4
第三章     平衡态临界相变 5
 3.1  临界慢化 5
 3.2  Cluster算法 6
第四章     短时动力学过程 7
 4.1  短时动力学 7
 4.2  自旋模型 8
4.2.1  Ising模型 8
4.2.2  XY模型及其他 9
      4.3  Ising模型的演化模拟 9
 4.3.1  初始态完全有序态的Ising模型 10
 4.3.2  初始态半有序态的Ising模型 11
 4.4  Ising模型的演化分析与讨论 12
 4.4.1  初始态完全有序态的Ising模型 12
 4.4.2  初始态半有序态的Ising模型 13
第五章     结论 14
致谢 15
参考文献 16

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