Phase transition and dynamical-parameter method in U(1) gauge theory

TL;DR

This paper introduces a dynamical-parameter method to study phase transitions in 4D U(1) lattice gauge theory, overcoming tunneling suppression issues in Monte Carlo simulations, and demonstrates its effectiveness on large lattices.

Contribution

The paper presents a new efficient method to determine parameters for dynamical monopole coupling, enabling reliable phase transition analysis in large lattice simulations.

Findings

Successfully applied to a 16^4 lattice.

Achieved equidistribution of configurations across the phase transition.

Circumvented tunneling barriers in Monte Carlo simulations.

Abstract

Monte Carlo simulations of the 4-dimensional compact U(1) lattice gauge theory in the neighborhood of the transition point are made difficult by the suppression of tunneling between the phases, which becomes very strong as soon as the volume of the lattice grows to any appreciable size. This problem can be avoided by making the monopole coupling a dynamical variable. In this manner one can circumvent the tunneling barrier by effectively riding on top of the peaks in the energy distribution which meet for sufficiently large monopole coupling. Here we present an efficient method for determining the parameters needed for this procedure, which can thus be implemented at low computational cost also on large lattices. This is particularly important for a reliable determination of the transition point. We demonstrate the working of our method on a 16^4 lattice. We obtain an equidistribution of configurations across the phase transition even for such a relatively large lattice size.