Scalar gauge-Higgs models with discrete Abelian symmetry groups

TL;DR

This paper studies the phase diagram and transition types of three-dimensional lattice gauge-Higgs models with discrete Abelian symmetry groups, confirming theoretical predictions with Monte Carlo simulations.

Contribution

It provides a detailed analysis of phase transitions in gauge-Higgs models with Z_N subgroups, including critical behavior and universality classes, supported by Monte Carlo results.

Findings

Transition lines follow Landau-Ginzburg-Wilson predictions.

Continuous transitions are in Ising and O(2) universality classes.

Monte Carlo simulations confirm theoretical predictions.

Abstract

We investigate the phase diagram and the nature of the phase transitions of three-dimensional lattice gauge-Higgs models obtained by gauging the Z_N subgroup of the global Z_q invariance group of the Z_q clock model (N is a submultiple of q). The phase diagram is generally characterized by the presence of three different phases, separated by three distinct transition lines. We investigate the critical behavior along the two transition lines characterized by the ordering of the scalar field. Along the transition line separating the disordered-confined phase from the ordered-deconfined phase, standard arguments within the Landau-Ginzburg-Wilson framework predict that the behavior is the same as in a generic ferromagnetic model with Z_p global symmetry, p being the ratio q/N. Thus, continuous transitions belong to the Ising and to the O(2) universality class for p=2 and p>3, respectively, while for p=3 only first-order transitions are possible. The results of Monte Carlo simulations confirm these predictions. There is also a second transition line, which separates two phases in which gauge fields are essentially ordered. Along this line we observe the same critical behavior as in the Z_q clock model, as it occurs in the absence of gauge fields.