Phase transitions in strongly coupled 3d Z(N) lattice gauge theories at finite temperature

TL;DR

This paper investigates phase transitions in 3D Z(N) lattice gauge theories at finite temperature, revealing two BKT-type transitions through analytical and Monte Carlo methods, and provides detailed critical behavior analysis.

Contribution

It introduces an analytical and numerical analysis of phase transitions in 3D Z(N) lattice gauge theories, identifying two BKT-type transitions and calculating critical indices.

Findings

Identification of two BKT-type phase transitions.

Explicit calculation of effective couplings in spin models.

Determination of critical indices and scaling behavior.

Abstract

We perform an analytical and numerical study of the phase transitions in three-dimensional Z(N) lattice gauge theories at finite temperature for N>4 exploiting equivalence of these models with a generalized version of the two-dimensional vector Potts models in the limit of vanishing spatial coupling. In this limit the Polyakov loops play the role of Z(N) spins. The effective couplings of these two-dimensional spin models are calculated explicitly. It is argued that the effective spin models have two phase transitions of BKT type. This is confirmed by large-scale Monte Carlo simulations. Using a cluster algorithm we locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices, compute the helicity modulus, the average action and the specific heat. A scaling formula for the critical points with N is proposed.