Physical properties of Polyakov loop geometrical clusters in SU(2) gluodynamics

TL;DR

This paper models the clustering behavior of Polyakov loops in SU(2) gluodynamics near the deconfinement transition using the liquid droplet model, revealing different surface tension behaviors as potential order parameters.

Contribution

It applies the liquid droplet model to lattice data of Polyakov loop clusters, extracting critical exponents and identifying surface tension as an order parameter for the phase transition.

Findings

Fisher exponent $ au$ = 1.806 ± 0.008 was determined.

Surface tension of clusters shows distinct temperature dependence below and above the transition.

Surface tension behaviors follow T^2 and T^4 laws in different cluster gases above the critical temperature.

Abstract

We apply the liquid droplet model to describe the clustering phenomenon in SU(2) gluodynamics, especially, in the vicinity of the deconfinement phase transition. In particular, we analyze the size distributions of clusters formed by the Polyakov loops of the same sign. Within such an approach this phase transition can be considered as the transition between two types of liquids where one of the liquids (the largest droplet of a certain Polyakov loop sign) experiences a condensation, while the other one (the next to largest droplet of opposite Polyakov loop sign) evaporates. The clusters of smaller sizes form two accompanying gases, and their size distributions are described by the liquid droplet parameterization. By fitting the lattice data we have extracted the value of Fisher exponent $\tau =$ 1.806 $\pm$ 0.008. Also we found that the temperature dependences of the surface tension of both gaseous clusters are entirely different below and above the phase transition and, hence, they can serve as an order parameter. The critical exponents of the surface tension coefficient in the vicinity of the phase transition are found. Our analysis shows that the temperature dependence of the surface tension coefficient above the critical temperature has a $T^2$ behavior in one gas of clusters and $T^4$ in the other one.