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研究生: 朱文萍
Zhu,Wen-Ping
論文名稱: 三維鐵磁性帕茲模型的相變現象
Phase Transitions of 3D Ferromagnetic Potts model
指導教授: 江府峻
學位類別: 碩士
Master
系所名稱: 物理學系
Department of Physics
論文出版年: 2019
畢業學年度: 107
語文別: 中文
論文頁數: 26
中文關鍵詞: 帕茲模型像變Wolff 演算法多層感知器卷積神經網絡
DOI URL: http://doi.org/10.6345/NTNU201900672
論文種類: 學術論文
相關次數: 點閱:108下載:27
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  • 本次研究主要探討了三維的帕茲模型 (Potts model) 的相變現象。我們使用了蒙地卡羅的方法,搭配 Wolff 演算法製造出不同溫度下的自旋組態,並且透過傳統方法中的能量圖和類神經網絡中的多層感知器和卷積神經網絡的計算來分析是否有產生相變現象。而在類神經網絡的部分,使用了低溫中的基態當作是訓練集,藉由最後的向量輸出y的長度|R|來判別臨界溫度Tc附近是否有發生相變現象。此種做法比起其它相關的類神經網絡在凝態物理的文獻中所使用的訓練 集,來得更有效率,並且也可以達到和已知文獻上相同的結果。

    This research mainly explores the phase transition of the three-dimensional q-states Potts model. We used Monte Carlo′s method and combined with the Wolff algorithm to create spin configurations at different temperatures. We analyze whether there is a phase change phenomenon by using the traditional idea and the calculations in multi-layer perceptron and convolutional neural network. In the part of the neural network, the ground state in the low temperature is used as the training set, and the critical temperature Tc is analyzed by examining whether there is a phase change phenomenon through the length |R| of the last output vector y. This method is not only more efficient than the training set used in other related works but also achieve the same results as known in the literature.

    Abstract 摘要 致謝 目次 Chapter 1 Model: 3D Ferromagnetic Potts model 1 1.1 Hamiltonian 1 1.2 Phase Transitions 2 Chapter 2 Algorithm 4 2.1 Wolff algorithm 4 Chapter 3 Method 7 3.1 傳統方法 7 3.2 人工神經網絡方法 8 3.2.1 多層感知器(Multi-layer Perceptron,MLP) 9 3.2.2 卷積神經網路(Convolutional Neural Network, CNN) 15 Chapter 4 數值結果 18 4.1 傳統方法的數值結果 18 4.2 類神經網絡的數值結果 20 4.2.1 多層感知器的分析結果 20 4.2.2 卷積神經網絡的分析結果 21 Chapter 5 討論 22 Reference 24

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