Random percolation as a gauge theory

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.

20 pages, 14 figures

References in corpus (2)

• Simulation of Potts models with real q and no critical slowing down
• Confinement-deconfinement and universal string effects from random percolation

Cited by in corpus (20)

• Thermodynamics of the QCD plasma and the large-N limit
• SU(N) gauge theories at large N
• Optical Abelian Lattice Gauge Theories
• Casimir scaling and renormalization of Polyakov loops in large-N gauge theories
• On the linear increase of the flux tube thickness near the deconfinement transition
• Introductory lectures to large-N QCD phenomenology and lattice results
• A percolation transition in Yang-Mills matter at finite number of colours
• The 4-D Layer Phase as a Gauge Field Localization: Extensive Study of the 5-D Anisotropic U(1) Gauge Model on the Lattice
• The static quark potential from a multilevel algorithm for the improved gauge action
• The confining string beyond the free-string approximation in the gauge dual of percolation
• Fluctuations of the baryonic flux-tube junction from effective string theory
• Classes of confining gauge field configurations
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Percolation as a confinement order parameter in ${\mathbb{Z}}_2$ lattice gauge theories
• Quarkyonic Percolation and deconfinement at finite density and number of colors
• The functional form of open Wilson lines in gauge theories coupled to matter
• A simple algorithm to test for linking to Wilson loops in percolation
• K-string tensions at finite temperature and integrable models
• Where is the confining string in random percolation
• On percolation in a generalized backbend process