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

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.

17 pages, 9 figures, minor corrections

References in corpus (4)

• Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
• Percolation and Critical Behaviour in SU(2) Gauge Theory
• Percolation and Deconfinement in SU(2) Gauge Theory
• Finite-size scaling and deconfinement transition: the case of 4D SU(2) pure gauge theory

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• Excluded-volume effects for a hadron gas in Yang-Mills theory
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Nuclear and Quark Matter at High Temperature
• Renormalized Polyakov loop in the Fixed Scale Approach
• Effective potential for Polyakov loops from a center symmetric effective theory in three dimensions
• Critical couplings and string tensions via lattice matching of RG decimations
• The $⟨A^2⟩$ Asymmetry and Longitudinal Propagator in Lattice $SU(2)$ Gluodynamics at $T\simeq T_c$