Monopole clusters and critical dynamics in four-dimensional U(1)

TL;DR

This paper studies monopole clusters in four-dimensional U(1) gauge theory, revealing their behavior near the phase transition and differences between Coulomb and confined phases, with implications for understanding critical dynamics.

Contribution

It provides a detailed analysis of monopole cluster properties and their evolution across the phase transition in 4D U(1) gauge theory, highlighting the absence of winding loops.

Findings

Small clusters dominate in Coulomb phase

Large cluster forms in confined phase

Winding monopole loops are absent in both phases

Abstract

We investigate monopoles in four-dimensional compact U(1) with Wilson action. We focus our attention on monopole clusters as they can be identified unambiguously contrary to monopole loops. We locate the clusters and determine their properties near the U(1) phase transition. The Coulomb phase is characterized by several small clusters, whereas in the confined phase the small clusters coalesce to one large cluster filling up the whole system. We find that clusters winding around the periodic lattice are absent within both phases and during the transition. However, within the confined phase, we observe periodically closed monopole loops if cooling is applied.