Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory

TL;DR

This study uses Monte Carlo simulations to analyze the critical behaviors of 3D lattice Abelian-Higgs models, revealing universal continuous phase transitions linked to a stable charged fixed point in the field theory.

Contribution

It demonstrates that the critical behaviors of lattice Abelian-Higgs models with compact gauge fields are universal and belong to the same class as noncompact models, clarifying the continuum limit conditions.

Findings

Transitions are continuous along the confined-deconfined line.

Universality class is consistent for different charges q ≥ 2.

Critical behaviors are governed by a stable charged fixed point.

Abstract

We investigate under which conditions the three-dimensional (3D) multicomponent Abelian-Higgs (AH) field theory (scalar electrodynamics) is the continuum limit of statistical lattice gauge models, i.e., when it characterizes the universal behavior at critical transitions occurring in these models. We perform Monte Carlo simulations of the lattice AH model with compact gauge fields and $N$-component scalar fields with charge $q\ge 2$ for $N=15$ and 25. Finite-size scaling analyses of the Monte Carlo data show that the transitions along the line separating the confined and deconfined phases are continuous and that they belong to the same universality class for any $q\ge 2$. Moreover, they are in the same universality class as the transitions in the lattice AH model with noncompact gauge fields along the Coulomb-to-Higgs transition line. We finally argue that these critical behaviors are described by the stable charged fixed point of the renormalization-group flow of the 3D AH field theory.