Random percolation as a gauge theory

TL;DR

This paper interprets 3D percolation on a lattice as a gauge theory, revealing universal flux tube effects, a spectrum of states akin to glueballs, and a deconfinement transition related to percolation thresholds.

Contribution

It introduces a gauge theory perspective to percolation, connecting topological linking, Wilson loops, and physical spectra with phenomena like confinement and deconfinement.

Findings

Wilson loops exhibit area law decay beyond percolation threshold

Spectrum of states resembles glueballs in gauge theories

Finite temperature deconfinement linked to cluster breaking

Abstract

Three-dimensional bond or site percolation theory on a lattice can be interpreted as a gauge theory in which the Wilson loops are viewed as counters of topological linking with random clusters. Beyond the percolation threshold large Wilson loops decay with an area law and show the universal shape effects due to flux tube quantum fluctuations like in ordinary confining gauge theories. Wilson loop correlators define a non-trivial spectrum of physical states of increasing mass and spin, like the glueballs of ordinary gauge theory. The crumbling of the percolating cluster when the length of one periodic direction decreases below a critical threshold accounts for the finite temperature deconfinement, which belongs to 2-D percolation universality class.