Percolation of Vortices in the 3D Abelian Lattice Higgs Model

TL;DR

This study uses high-precision Monte Carlo simulations to analyze vortex percolation in the 3D Abelian lattice Higgs model, revealing how vortex networks behave across different phase transition regions.

Contribution

It demonstrates that vortex percolation correlates with phase boundaries and exhibits finite-size scaling, with critical behavior aligning with the random percolation universality class.

Findings

Vortices percolate at the phase boundary during first-order transitions.

Vortex percolation persists in crossover regions without a first-order transition.

Percolation observables exhibit finite-size scaling and critical exponents match random percolation.

Abstract

The compact Abelian Higgs model is simulated on a cubic lattice where it possesses vortex lines and pointlike magnetic monopoles as topological defects. The focus of this high-precision Monte Carlo study is on the vortex network, which is investigated by means of percolation observables. In the region of the phase diagram where the Higgs and confinement phases are separated by a first-order transition, it is shown that the vortices percolate right at the phase boundary, and that the first-order nature of the transition is reflected by the network. In the crossover region, where the phase boundary ceases to be first order, the vortices are shown to still percolate. In contrast to other observables, the percolation observables show finite-size scaling. The exponents characterizing the critical behavior of the vortices in this region are shown to fall in the random percolation universality class.