三維鐵磁性帕茲模型的相變現象

Abstract

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.