Extracting Critical Exponent by Finite-Size Scaling with Convolutional Neural Networks

TL;DR

This paper introduces a finite-size scaling method using convolutional neural networks to accurately extract critical exponents in phase transitions, demonstrating its effectiveness across different models like quantum Hall, Ising, and Potts.

Contribution

The study presents a novel neural network-based finite-size scaling approach for quantitatively analyzing critical behavior in various condensed matter models.

Findings

Neural network accurately learns the critical exponent for quantum Hall transition.

Method successfully applies to Ising and Potts models with different physics.

Critical exponents obtained are consistent with traditional methods.

Abstract

Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we propose a finite-size scaling approach based on a convolutional neural network and analyze the critical behavior of a quantum Hall plateau transition. The localization length critical exponent learned by the neural network is consistent with the value obtained by conventional approaches. We show that the general-purposed method can be used to extract critical exponents in models with drastically different physics and input data, such as the two-dimensional Ising model and 4-state Potts model.