Optimized Machine Learning Methods for Studying the Thermodynamic Behavior of Complex Spin Systems

TL;DR

This study demonstrates the effectiveness of convolutional neural networks in analyzing phase transitions and thermodynamic properties of complex spin systems, providing accurate critical temperature predictions without retraining.

Contribution

It introduces CNN-based classifiers for various spin models, achieving high accuracy and efficiency in identifying phase states and critical points.

Findings

CNN classifiers outperform fully connected networks in RMSE

Temperature profiles intersect near theoretical critical temperatures

Method accurately predicts critical temperature for kagome lattice

Abstract

This paper presents a systematic study of the application of convolutional neural networks (CNNs) as an efficient and versatile tool for the analysis of critical and low-temperature phase states in spin system models. The problem of calculating the dependence of the average energy on the spatial distribution of exchange integrals for the Edwards-Anderson model on a square lattice with frustrated interactions is considered. We further construct a single convolutional classifier of phase states of the ferromagnetic Ising model on square, triangular, honeycomb, and kagome lattices, trained on configurations generated by the Swendsen-Wang cluster algorithm. Computed temperature profiles of the averaged posterior probability of the high-temperature phase form clear S-shaped curves that intersect in the vicinity of the theoretical critical temperatures and allow one to determine the critical temperature for the kagome lattice without additional retraining. It is shown that convolutional models substantially reduce the root-mean-square error (RMSE) compared with fully connected architectures and efficiently capture complex correlations between thermodynamic characteristics and the structure of magnetic correlated systems.