Neural Network Approach to Scaling Analysis of Critical Phenomena

TL;DR

This paper introduces a neural network-based regression method for analyzing critical phenomena, offering high accuracy and computational efficiency in determining universality classes from data.

Contribution

It presents a novel neural network approach for finite-size scaling analysis, improving accuracy and reducing computational complexity compared to existing methods.

Findings

Accurately determines critical values in Ising model and percolation.

Computational complexity is linear in data points.

Outperforms polynomial regression and Gaussian process regression.

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.