No coincidence of center percolation and deconfinement in SU(4) lattice gauge theory

TL;DR

This paper investigates the behavior of center sectors in SU(4) lattice gauge theory at finite temperature, revealing that deconfinement does not correspond to a percolation transition of center clusters, unlike in SU(2) or SU(3).

Contribution

It demonstrates that, in SU(4) gauge theory, deconfinement is not associated with center cluster percolation, contrasting with lower SU(N) theories.

Findings

Deconfinement in SU(4) is not a percolation transition.

Center clusters do not percolate at the deconfinement point.

This behavior differs from SU(2) and SU(3) gauge theories.

Abstract

We study the behavior of center sectors in pure SU(4) lattice gauge theory at finite temperature. The center sectors are defined as spatial clusters of neighboring sites with values of their local Polyakov loops near the same center elements. We study the connectedness and percolation properties of the center clusters across the deconfinement transition. We show that for SU(4) gauge theory deconfinement cannot be described as a percolation transition of center clusters, a finding which is different from pure SU(2) or pure SU(3) Yang Mills theory, where the percolation description even allows for a continuum limit.