短時動力學方法及應用

應用物理學論文編號:WLX112  字數:8482,頁數:19

目  錄
中文摘要 i
英文摘要 ii
目錄 iii
第一章     緒論  1
第二章     Monte Carlo方法  2
 2.1  Monte Carlo隨機抽樣基本方法 2
2.1.1  簡單抽樣的Monte Carlo方法 2
2.1.2  重要抽樣的Monte Carlo方法 2
 2.2  Metropolis算法 2
 2.3  Heat-bath算法 4
第三章     平衡態臨界相變 5
 3.1  臨界慢化 5
 3.2  Cluster算法 6
第四章     短時動力學過程 7
 4.1  短時動力學 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模型的演化模擬 9
 4.3.1  初始態完全有序態的Ising模型 10
 4.3.2  初始態半有序態的Ising模型 11
 4.4  Ising模型的演化分析與討論 12
 4.4.1  初始態完全有序態的Ising模型 12
 4.4.2  初始態半有序態的Ising模型 13
第五章     結論 14
致謝 15
參考文獻 16

摘    要
 相變和臨界現象是系統由一種穩定狀態向另一種穩定狀態的突變過程，是統計物理和凝聚態物理的重要研究對象。近年來，隨著計算機技術的發展，數值模擬已成為研究相變與臨界現象的一種重要的方法。本文采用短時動力學方法模擬處于臨界相變下的二維Ising 模型的自旋。
 首先從理論上討論了Monte Carlo方法和數值模擬方法，引入了重要抽樣、細致平衡條件、 Metropolis 算法和Heat-bath算法等。然后從理論上闡述了各類自旋模型及其平衡態和非平衡態，引入了臨界慢化、cluster算法、Ising模型等。在此基礎上，我們用Monte Carlo方法模擬了二維 Ising 模型相變，得到了隨時間的演化規律且進行了相關討論。
關鍵詞： 短時動力學  臨界慢化  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