Multicomponent gauge-Higgs models with discrete Abelian gauge groups

TL;DR

This paper studies a multicomponent gauge-Higgs model with discrete Abelian gauge groups, revealing how the universality class of phase transitions depends on the scalar fields and gauge field nature, with transitions varying from continuous to first-order.

Contribution

It demonstrates that the universality class is determined by scalar field behavior and independent of the gauge group q for q>=3, and shows how replacing U(1) with Z_q gauge fields affects transition order.

Findings

Universality class depends on scalar fields, not gauge fields.

Transitions are continuous for certain scalar configurations, independent of q.

Replacing U(1) with Z_q gauge fields can change transition order from continuous to first-order.

Abstract

We consider a variant of the charge-Q compact Abelian-Higgs model, in which an Nf-dimensional complex vector is coupled with an Abelian Z_q gauge field. For Nf=2 and Q=1 we observe several transition lines that belong to the O(4), O(3), and O(2) vector universality classes, depending on the symmetry breaking pattern at the transition. The universality class is independent of $q$ as long as q>=3. The universality class of the transition is uniquely determined by the behavior of the scalar fields; gauge fields do not play any role. We also investigate the system for Nf=15 and Q=2. In the presence of U(1) gauge fields, the system undergoes transitions associated with charged fixed points of the Abelian-Higgs field theory. These continuous transitions turn into first-order ones when the U(1) gauge fields are replaced by the discrete Z_q fields: in the present compact model charged transitions appear to be very sensitive to the nature of the gauge fields