摘要
本論文主要是利用蒙地卡羅法來模擬二維的Potts model在外場中由一階相變轉換成二階相變的情形。
6階Potts model在二維純晶格中，系統是一階相變。但若隨機加入外場時，會改變相變的階數。我們的蒙地卡羅模擬顯示當外加場大於0.02時，系統將由一階相變轉變為二階相變。

Abstract
In this paper, we study the nature of phase transition of the two-dimensional six-state Potts model under the external random magnetic field.
The six-state Potts model exist temperature-dependent first-order phase transition. When the external random field is applied, the nature of phase can be altered from first-order to second-order.By employing the Monte Carlo simulation method, we inspected the energy histogram and Binder parameter of the six-state Potts model under the external random magnetic field. According to our analyses, the evidences reveal that the phase transition does not change until the external magnetic field is greater then 0.02

目錄

第一章 緒論
1-1 相變
1-1-1 何謂相變-----------------------------------------------5
1-1-2 相變的因素---------------------------------------------5
1-1-3 相變的分類 --------------------------------------------6
1-2 統計模型
1-2-1 伊辛模型(Ising model)--------------------------------- 9
1-2-2 帕茲模型(Potts model)--------------------------------- 12
1-3 帕茲模型的實驗證明-----------------------------------------15
1-4 隨機缺陷的帕茲模型-----------------------------------------18
第二章 模擬方法
2-1 蒙地卡羅法
2-1-1 簡介--------------------------------------------------21
2-1-2 理論基礎----------------------------------------------22
2-2 亂數產生器-------------------------------------------------27
第三章 模擬步驟---------------------------------------------------29
第四章 結果與分析-------------------------------------------------32
第五章 討論-------------=-----------------------------------------34
參考資料---------------------------------------------------36
附圖(結果部份)

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