Neural Network Approach to Scaling Analysis of Critical Phenomena

Abstract

Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. There are several methods to determine this universality class from data. As methods performing collapse plots onto scaling functions, polynomial regression, which is less accurate, and Gaussian process regression, which provides high accuracy and flexibility but is computationally heavy, have been proposed. In this paper, we propose a regression method using a neural network. The computational complexity is only linear in the number of data points. We demonstrate the proposed method for the finite-size scaling analysis of critical phenomena on the two-dimensional Ising model and bond percolation problem to confirm the performance. This method efficiently obtains the critical values with accuracy in both cases.

arXiv comment10 pages, 10 figures, code implementation is available at https://github.com/yonesuke/jaxfss and https://github.com/KenjiHarada/FSS-tools

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