Phase determination with and without deep learning.

IF 2.2 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS
Burak Çivitcioğlu, Rudolf A Römer, Andreas Honecker
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引用次数: 0

Abstract

Detection of phase transitions is a critical task in statistical physics, traditionally pursued through analytic methods and direct numerical simulations. Recently, machine-learning techniques have emerged as promising tools in this context, with a particular focus on supervised and unsupervised learning methods, along with nonlearning approaches. In this paper, we study the performance of unsupervised learning in detecting phase transitions in the J_{1}-J_{2} Ising model on the square lattice. The model is chosen due to its simplicity and complexity, thus providing an understanding of the application of machine-learning techniques in both straightforward and challenging scenarios. We propose a simple method based on a direct comparison of configurations. The reconstruction error, defined as the mean-squared distance between two configurations, is used to determine the critical temperatures. The results from the comparison of configurations are contrasted with those of the configurations generated by variational autoencoders. Our findings highlight that for certain systems a simpler method can yield results comparable to more complex neural networks. This paper contributes to the broader understanding of machine-learning applications in statistical physics and introduces an efficient approach to the detection of phase transitions using machine determination techniques.

有和没有深度学习的阶段确定。
相变的检测是统计物理中的一项关键任务,传统上是通过分析方法和直接数值模拟来实现的。最近,机器学习技术在这方面已经成为有前途的工具,特别关注监督和无监督学习方法,以及非学习方法。本文研究了方形晶格上J_{1}-J_{2} Ising模型中无监督学习检测相变的性能。选择该模型是因为它的简单性和复杂性,从而提供了对机器学习技术在简单和具有挑战性的场景中的应用的理解。我们提出了一种基于构型直接比较的简单方法。重构误差定义为两种构型之间的均方距离,用于确定临界温度。将构形结果与变分自编码器生成的构形结果进行了对比。我们的研究结果强调,对于某些系统,更简单的方法可以产生与更复杂的神经网络相当的结果。本文有助于更广泛地理解机器学习在统计物理中的应用,并介绍了一种使用机器测定技术检测相变的有效方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical Review E
Physical Review E PHYSICS, FLUIDS & PLASMASPHYSICS, MATHEMAT-PHYSICS, MATHEMATICAL
CiteScore
4.50
自引率
16.70%
发文量
2110
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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