Finite temperature SU(2) gauge theory: critical coupling and universality class

TL;DR

This paper investigates the critical behavior of SU(2) gauge theory at finite temperature, confirming its universality class matches the 3D Ising model and analyzing scaling violations across coupling regimes.

Contribution

It provides high precision measurements of critical couplings, Binder cumulants, and string tensions for various lattice sizes, confirming universality and examining scaling violations.

Findings

Critical coupling values match 3D Ising universality class.

Observed less than 10% scaling violation across coupling regimes.

Measured string tensions and analyzed the T_c/√σ ratio scaling.

Abstract

We examine SU(2) gauge theory in 3+1 dimensions at finite temperature in the vicinity of critical point. For various lattice sizes in time direction ($N_\tau=1,2,4,8$) we extract high precision values of the inverse critical coupling and critical values of the 4-th order cumulant of Polyakov loops (Binder cumulant). We check the universality class of the theory by comparing the cumulant values to that of the 3D Ising model and find very good agreement. The Polyakov loop correlators for the indicated lattices are also measured and the string tension values extracted. The high precision values of critical coupling and string tension allow us to study the scaling of dimensionless $T_c/\sqrt{\sigma}$ ratio. The violation of scaling by <10% is observed as the coupling is varied from weak to strong coupling regime.