Phase structure of 3D Z(N) lattice gauge theories at finite temperature: large-N and continuum limits

TL;DR

This paper numerically investigates the phase structure of 3D Z(N) lattice gauge theories at finite temperature for various N, analyzing phase transitions, critical indices, and continuum scaling to deepen understanding of their thermodynamic behavior.

Contribution

It provides a comprehensive numerical analysis of phase transitions and critical behavior in 3D Z(N) lattice gauge theories at finite temperature, including scaling laws near the continuum limit.

Findings

Identified phase transition points for N=5,6,8,12,13,20.

Determined critical indices for each N.

Proposed scaling of critical points with N.

Abstract

We study numerically three-dimensional Z(N) lattice gauge theories at finite temperature, for N = 5, 6, 8, 12, 13 and 20 on lattices with temporal extension $N_t$ = 2, 4, 8. For each model, we locate phase transition points and determine critical indices. We propose also the scaling of critical points with N. The data obtained enable us to verify the scaling near the continuum limit for the Z(N) models at finite temperatures.