Geometry of the monopole clusters at different scales
V.G. Bornyakov, P.Yu. Boyko, M.I. Polikarpov, V.I. Zakharov
TL;DR
This study investigates the geometric properties of monopole clusters in SU(2) lattice gauge theory, revealing scale-dependent behaviors and correlations that inform understanding of confinement mechanisms.
Contribution
It provides the first detailed analysis of monopole cluster geometry across multiple scales, highlighting the transition from random walk behavior to long-range correlations.
Findings
Short clusters behave as random walks at small scales.
Long-range correlations emerge at the hadronic scale.
Percolating cluster does not resemble a random walk at the hadronic scale.
Abstract
We present results of measurements of various geometrical characteristics of the monopole clusters in the maximally Abelian projection of SU(2) lattice gauge theory. We observe scaling for the observables tested. Short clusters correspond to random walks at small scale but have long-range correlations at the hadronic scale. On the other hand, the percolating cluster at the hadronic scale does not correspond to a random walk.
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