Monopole clusters at short and large distances

TL;DR

This paper investigates the geometrical properties of monopole clusters in SU(2) lattice gauge theory, revealing scaling behaviors, the transition from random walks to correlated trajectories, and long-range correlations linked to two-dimensional surfaces.

Contribution

It provides new insights into the structure and correlations of monopole clusters, including their scaling, geometric characteristics, and association with two-dimensional surfaces.

Findings

Scaling observed for monopole segment lengths and correlators

Monopole trajectories transition from random walks to correlated structures at hadronic scales

Evidence of long-range correlations linked to two-dimensional surfaces

Abstract

We present measurements of various geometrical characteristics of monopole clusters in SU(2) lattice gauge theory. The maximal Abelian projection is employed and both infinite, or percolating cluster and finite clusters are considered. In particular, we observe scaling for average length of segments of the percolating cluster between self-crossings, correlators of vacuum monopole currents, angular correlation between links along trajectories. Short clusters are random walks and their spectrum in length corresponds to free particles. At the hadronic scale, on the other hand, the monopole trajectories are no longer random walks. Moreover, we argue that the data on the density of finite clusters suggest that there are long-range correlations between finite clusters which can be understood as association of the clusters with two-dimensional surfaces, whose area scales.