Multi-Higgs U(1) Lattice Gauge Theory in Three Dimensions

TL;DR

This paper investigates the phase structure of three-dimensional compact U(1) lattice gauge theory with multiple Higgs fields, revealing different phase transition behaviors depending on the number of Higgs fields and coupling parameters.

Contribution

It provides a numerical analysis of the phase transitions in multi-Higgs U(1) lattice gauge theory, identifying second-order and first-order transition lines for different Higgs field counts.

Findings

For N=2, a second-order phase transition line separates confinement and Higgs phases.

For N=3, the critical line splits into regions with first-order and second-order transitions.

Transition behavior depends on the Higgs field number and coupling parameters.

Abstract

We study the three-dimensional compact U(1) lattice gauge theory with $N$ Higgs fields numerically. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. For N=2, the system has a second-order phase transition line $\tilde{c}_1(c_2)$ in the $c_2$(gauge coupling)$-c_1$(Higgs coupling) plane, which separates the confinement phase and the Higgs phase. For N=3, the critical line is separated into two parts; one for $c_2 \alt 2.25$ with first-order transitions, and the other for $c_2 \agt 2.25$ with second-order transitions.