Super-resolving the Ising model with convolutional neural networks

TL;DR

This paper introduces a deep learning approach to enhance lattice spin configurations in the Ising model, enabling accurate predictions of thermodynamic properties and critical exponents for larger system sizes than trained on.

Contribution

It presents a novel super-resolution method using convolutional neural networks to invert real-space renormalization, extending the analysis of the Ising model to larger lattices.

Findings

Super-resolution reproduces thermodynamic observables accurately.

The method predicts properties for larger lattices than training data.

Extrapolated critical exponents agree with theoretical values.

Abstract

Machine learning is becoming widely used in condensed matter physics. Inspired by the concept of image super-resolution, we propose a method to increase the size of lattice spin configurations using deep convolutional neural networks. Through supervised learning on Monte Carlo (MC) generated spin configurations, we train networks that invert real-space renormalization decimations. We demonstrate that super-resolution can reproduce thermodynamic observables that agree with MC calculations for the one and two-dimensional Ising model at various temperatures. We find that it is possible to predict thermodynamic quantities for lattice sizes larger than those used in training by extrapolating the parameters of the network. We use this method to extrapolate the exponents of the 2D Ising critical point towards the thermodynamic limit, which results in good agreement with theory.