Detecting the 3D Ising model phase transition with a ground-state-trained autoencoder

TL;DR

This paper presents a deep learning autoencoder trained solely on ground-state configurations to detect phase transitions and critical behavior in the 3D Ising model, without prior knowledge of key parameters.

Contribution

It introduces a novel one-class autoencoder approach that identifies critical points and exponents from ground-state data alone, bypassing traditional methods.

Findings

Successfully estimated the critical temperature as 4.5128(58).

Determined the correlation-length critical exponent as 0.63(27).

Demonstrated the autoencoder's sensitivity to phase transitions across lattice sizes.

Abstract

We develop a one-class, deep-learning framework to detect the phase transition and recover critical behavior of the 3D Ising model. A 3D convolutional neural network autoencoder (CAE) is trained on ground-state configurations only, without prior knowledge of the critical temperature, the Hamiltonian, or the order parameter. After training, the model is applied to Monte Carlo configurations across a wide temperature range and different lattice sizes. The mean-square reconstruction error is shown to be sensitive to the transition. Finite-size scaling of the peak location for the reconstruction error susceptibility yields the critical temperature $T_c=4.5128(58)$ and the correlation-length critical exponent $\nu=0.63(27)$, consistent with results from the literature. Our results show that a one-class CAE, trained on zero-temperature configurations only, can recover nontrivial critical behavior of the 3D Ising model.