Three-dimensional finite temperature Z$_2$ gauge theory with tensor network scheme

TL;DR

This paper employs tensor network methods to analyze finite temperature Z$_2$ gauge theory in 2+1 dimensions, accurately determining the transition temperature and critical exponent, confirming the Svetitsky-Yaffe conjecture.

Contribution

It introduces a tensor network scheme to study finite temperature Z$_2$ gauge theory, achieving high-precision results for critical properties.

Findings

Transition temperature accurately determined

Critical exponent $ u$ consistent with theory

Finite size scaling up to $N_{\sigma}=4096$

Abstract

We apply a tensor network scheme to finite temperature Z$_2$ gauge theory in 2+1 dimensions. Finite size scaling analysis with the spatial extension up to $N_{\sigma}=4096$ at the temporal extension of $N_\tau=2,3,5$ allows us to determine the transition temperature and the critical exponent $\nu$ at high level of precision, which shows the consistency with the Svetitsky-Yaffe conjecture.