Critical temperature of the classical XY model via autoencoder latent space sampling

TL;DR

This paper introduces a machine learning approach using autoencoders to identify the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model by analyzing vortex density in the latent space.

Contribution

The study presents a novel autoencoder-based method to detect phase transitions in the XY model through latent space sampling, offering a new tool for topological phase transition analysis.

Findings

Successfully identified the critical temperature of the BKT transition.

Demonstrated the effectiveness of latent space sampling for phase transition detection.

Provided a new machine learning framework for analyzing topological phenomena.

Abstract

The classical XY model has been consistently studied since it was introduced more than six decades ago. Of particular interest has been the two-dimensional spin model's exhibition of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This topological phenomenon describes the transition from bound vortex-antivortex pairs at low temperatures to unpaired or isolated vortices and anti-vortices above some critical temperature. In this work we propose a novel machine learning based method to determine the emergence of this phase transition. An autoencoder was used to map states of the XY model into a lower dimensional latent space. Samples were taken from this latent space to determine the thermal average of the vortex density which was then used to determine the critical temperature of the phase transition.