Kertesz Line in the Three-Dimensional Compact U(1) Lattice Higgs Model

TL;DR

This study uses Monte Carlo simulations to explore the phase structure of the three-dimensional compact U(1) lattice Higgs model, revealing a phase boundary with a Kertesz line where thermodynamic quantities remain nonsingular.

Contribution

It provides the first detailed numerical analysis of the Kertesz line in the 3D compact U(1) lattice Higgs model, identifying the nature of phase transitions and the role of vortices.

Findings

Identified a phase boundary between Higgs and confined phases.

Discovered a Kertesz line with nonsingular thermodynamic behavior.

Showed the phase boundary ends at a critical point.

Abstract

The three-dimensional lattice Higgs model with compact U(1) gauge symmetry and unit charge is investigated by means of Monte Carlo simulations. The full model with fluctuating Higgs amplitude is simulated, and both energy as well as topological observables are measured. The data show a Higgs and a confined phase separated by a well-defined phase boundary, which is argued to be caused by proliferating vortices. For fixed gauge coupling, the phase boundary consists of a line of first-order phase transitions at small Higgs self-coupling, ending at a critical point. The phase boundary then continues as a Kertesz line across which thermodynamic quantities are nonsingular. Symmetry arguments are given to support these findings.