Critical behavior and continuum scaling of $3D$ $Z(N)$ lattice gauge theories

TL;DR

This paper investigates the critical behavior and continuum scaling of 3D $Z(N)$ lattice gauge theories at finite temperature, analyzing phase transitions and critical indices for various N and temporal extents.

Contribution

It provides a numerical study of phase transitions and critical indices in 3D $Z(N)$ lattice gauge theories, proposing a scaling of critical points with N and verifying continuum limit scaling.

Findings

Critical points scale with N as proposed.

Critical indices determined for multiple N values.

Scaling near the continuum limit verified.

Abstract

Three-dimensional $Z(N)$ lattice gauge theories are studied numerically at finite temperature for $N$ = 5, 6, 8, 12, 13, 20 and for $N_t$=2,4,8. For each model the location of phase transitions and its critical indices are determined. The scaling of critical points with $N$ is proposed. The data obtained enable us to verify the scaling near the continuum limit for the $Z(N)$ models at finite temperatures.