Monopoles in Compact U(1) -- Anatomy of the Phase Transition

TL;DR

This paper investigates the nature of the phase transition in compact U(1) gauge theory, showing that monopole loops are not the cause of the first order transition, challenging previous assumptions.

Contribution

It demonstrates that monopole loops are not responsible for the first order phase transition in compact U(1), using boundary condition manipulations and lattice size analysis.

Findings

First order transition persists despite monopole suppression.

Double peak structure reappears at larger lattice sizes.

Monopoles are not the primary driver of the phase transition.

Abstract

We present evidence that the existence of a first order phase transition in compact U(1) with Wilson action is not related to monopole loops wrapping around the toroidal lattice, as has been previously suggested. Our analysis is based on the suppression of such loops by `soft boundary conditions' that correspond to an infinitely large chemical potential for the monopoles on the boundary, during the updating process. It is observed that the double peak structure characteristic for the first order phase transition reappears at sufficiently large lattice sizes and separations from the lattice boundary.