Computing critical exponents in 3D Ising model via pattern recognition/deep learning approach

TL;DR

This paper combines finite-size scaling analysis and deep learning to compute critical exponents in the 3D Ising model, demonstrating effective classification of spin conformations with high accuracy.

Contribution

It introduces a novel deep learning approach using CNNs to classify spin states into latent classes, aiding the analysis of critical phenomena in the 3D Ising model.

Findings

Deep learning reduces thermodynamic data to six latent classes.

CNN achieves 92% train accuracy and 68.75% test accuracy on conformations.

Method shows promise but requires further validation for critical exponent estimation.

Abstract

In this study, we computed three critical exponents ($\alpha, \beta, \gamma$) for the 3D Ising model with Metropolis Algorithm using Finite-Size Scaling Analysis on six cube length scales (L=20,30,40,60,80,90), and performed a supervised Deep Learning (DL) approach (3D Convolutional Neural Network or CNN) to train a neural network on specific conformations of spin states. We find one can effectively reduce the information in thermodynamic ensemble-averaged quantities vs. reduced temperature t (magnetization per spin $<m>(t)$, specific heat per spin $<c>(t)$, magnetic susceptibility per spin $<\chi>(t)$) to \textit{six} latent classes. We also demonstrate our CNN on a subset of L=20 conformations and achieve a train/test accuracy of 0.92 and 0.6875, respectively. However, more work remains to be done to quantify the feasibility of computing critical exponents from the output class labels (binned $m, c, \chi$) from this approach and interpreting the results from DL models trained on systems in Condensed Matter Physics in general.