Distribution of Magnetic Monopoles within cubes in Compact QED

TL;DR

This paper investigates the spatial distribution of magnetic monopoles in lattice U(1) gauge theory, revealing their tendency to localize at cube centers or interfaces, consistent with potential minima and maxima.

Contribution

It provides a detailed localization method for monopoles in Monte Carlo configurations and compares their distribution with the monopole-antimonopole potential.

Findings

Monopoles mainly located at cube centers or interfaces

Distribution aligns with potential minima and maxima

Supports previous potential measurements

Abstract

Earlier investigations showed local minima in the monopole-antimonopole potential in U(1) gauge theory on the lattice. In this paper we localize monopoles of Monte-Carlo configurations. A statistical analysis of localization measurements gives us the probability density which we compare with the potential found in [1]. We find the monopoles mainly located either in the center of three-dimensional cubes or on the interface between two cubes. This agrees with the position of minima and maxima of the monopole-antimonopole potential.