Multicomponent compact Abelian-Higgs lattice models

TL;DR

This study explores the phase transitions and critical behavior of three-dimensional multicomponent Abelian-Higgs lattice models, revealing continuous and first-order transitions depending on the number of components and gauge coupling strength.

Contribution

It provides the first detailed analysis of the phase diagram and transition nature for N=2 and N=4 in these models, highlighting the independence of transition type from gauge coupling.

Findings

For N=2, the transition is continuous and in the Heisenberg universality class.

For N=4, the transition is first-order.

Gauge correlations are always massive, with no critical gauge fluctuations.

Abstract

We investigate the phase diagram and critical behavior of three-dimensional multicomponent Abelian-Higgs models, in which an N-component complex field z_x^a of unit length and charge is coupled to compact quantum electrodynamics in the usual Wilson lattice formulation. We determine the phase diagram and study the nature of the transition line for N=2 and N=4. Two phases are identified, specified by the behavior of the gauge-invariant local composite operator Q_x^{ab} = \bar{z}_x^a z_x^b - \delta^{ab}/N, which plays the role of order parameter. In one phase, we have \langle Q_x^{ab}\rangle =0, while in the other Q_x^{ab} condenses. Gauge correlations are never critical: gauge excitations are massive for any finite coupling. The two phases are separated by a transition line. Our numerical data are consistent with the simple scenario in which the nature of the transition is independent of the gauge coupling. Therefore, for any finite positive value of the gauge coupling, we predict a continuous transition in the Heisenberg universality class for N=2 and a first-order transition for N=4. However, notable crossover phenomena emerge for large gauge couplings, when gauge fluctuations are suppressed. Such crossover phenomena are related to the unstable O(2N) fixed point, describing the behavior of the model in the infinite gauge-coupling limit.