對二維易辛模型非平衡相變的綜合研究

Abstract

利用蒙地卡羅法以及監督式神經網路，我們研究在二維棋盤狀易辛模型的非平衡相變。非平衡相變是透過令模擬該模型時使用的Metropolis 演算法違反細緻平衡條件達成的。此篇研究所使用的神經網路模型是直接取自於過往研究曾經訓練過的模型，換句話說本次研究沒有訓練任何模型。值得注意的事情是蒙地卡羅法以及監督式神經網路獲得結果是一樣的。具體來說，取得的結果表明所研究的相變是屬於二維易辛普遍類別。此篇研究也同時詳細探討了傳統捲積神經網路模型(CNN)的性能會如何受到訓練過程以及訓練集相關的參數的影響。經過論證過，我們得到的結論為本研究所使用神經網路模型在估計臨界點比文獻中所使用的傳統CNN更有效率以及穩定。本摘要及本碩士論文是根據以下之期刊論文的內容而編寫而成的.Eur. Phys. J. Plus (2024) 139:776 https://doi.org/10.1140/epjp/s13360-024-05563-8We study the non-equilibrium phase transitions associated with the 2-dimensional (2D) Ising model on the square lattice using both the methods of Monte Carlo (MC) calculations and neural networks (NN). The non-equilibrium phase transitions are triggered by introducing a parameter that breaks the condition of detailed balance in the MC simulations. The NN considered here isa simple unconventional multilayer perceptron (MLP) directly adopted from previous studies. In other words, no NN training is conducted in this study. Based on careful analyses, we confirm that the investigated non-equilibrium phase transitions are governed by the 2D Ising universality class. We also study these targeted phase transitions with a conventional convolutional neural network (CNN). The obtained results indicate that the predictions from the used CNN may be affected by some NN-related parameters. We demonstrate that our unconventional MLP is more efficient than the employed conventional CNN, and the related predictions are more stable as well.This abstract and the contents of this thesis are based on Eur. Phys. J. Plus (2024) 139:776 https://doi.org/10.1140/epjp/s13360-024-05563-8