Geometrical clusterization of Polyakov loops in SU(2) lattice gluodynamics

TL;DR

This paper analyzes the phase transition in SU(2) gluodynamics by applying the liquid droplet formula to geometrical clusters of Polyakov loops, revealing the transition as a liquid-liquid condensation process and identifying surface tension as an order parameter.

Contribution

It introduces a geometrical cluster analysis using the liquid droplet formula to explain the deconfinement transition in SU(2) gluodynamics and connects the universality class to a nuclear liquid-gas model.

Findings

Surface tension of gaseous clusters serves as an order parameter.

Fisher topological exponent $ au$ is approximately 1.806.

The universality class matches that of the nuclear liquid-gas phase transition.

Abstract

The liquid droplet formula is applied to an analysis of the properties of geometrical (anti)clusters formed in SU(2) gluodynamics by the Polyakov loops of the same sign. Using this approach, we explain the phase transition in SU(2) gluodynamics as a transition between two liquids during which one of the liquid droplets (the largest cluster of a certain Polyakov loop sign) experiences a condensation, while the droplet of another liquid (the next to the largest cluster of the opposite sign of Polyakov loop) evaporates. The clusters of smaller sizes form two accompanying gases, which behave oppositely to their liquids. The liquid droplet formula is used to analyze the size distributions of the gaseous (anti)clusters. The fit of these distributions allows us to extract the temperature dependence of surface tension and the value of Fisher topological exponent $\tau$ for both kinds of gaseous clusters. It is shown that the surface tension coeficient of gaseous (anti)clusters can serve as an order parameter of the deconfinement phase transition in SU(2) gluodynamics. The Fisher topological exponent $\tau$ of clusters and anticlusters is found to have the same value $1.806 \pm 0.008$. This value disagrees with the famous Fisher droplet model, but it agrees well with an exactly solvable model of the nuclear liquid-gas phase transition. This finding may evidence for the fact that the SU(2) gluodynamics and this exactly solvable model of nuclear liquid-gas phase transition are in the same universality class.