Application of the Variational Autoencoder to Detect the Critical Points of the Anisotropic Ising Model

TL;DR

This paper demonstrates that variational autoencoders can accurately identify critical points and phase diagrams of anisotropic Ising models, including potential applications to quantum systems, without explicit order parameters.

Contribution

It extends the application of variational autoencoders to anisotropic models and provides evidence for their use in analyzing quantum systems via Monte Carlo methods.

Findings

Successfully reproduces phase diagram for anisotropic Ising model

Locates critical points exactly using VAE without explicit order parameters

Suggests applicability to quantum spin models through partition function mapping

Abstract

We generalize the previous study on the application of variational autoencoders to the two-dimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for the entire range of anisotropic coupling. This presents an excellent testbed for the validity of using a variational autoencoder to characterize an anisotropic classical model. We reproduce the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Considering that the partition function of $(d+1)$-dimensional anisotropic models can be mapped to that of the $d$-dimensional quantum spin models, the present study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems via Quantum Monte Carlo.