A Study of Finite Temperature Gauge Theory in (2+1) Dimensions

TL;DR

This study investigates the finite-temperature deconfinement transition in SU(2) and SU(3) pure gauge theories in (2+1) dimensions. Using lattice simulations with the Wilson action, it determines the critical couplings and exponents via Polyakov-loop observables and finite-size scaling, and computes the zero-temperature string tension from Wilson loops with APE smearing. The resulting $T_c/\sqrt{\sigma}$ values show SU(3) in quantitative agreement with the Nambu-Goto string model, while SU(2) deviates by about 7%. The work confirms universality predictions from reduced models and provides precise characterizations of the string tension across couplings.

Abstract

We determine the critical couplings and the critical exponents of the finite temperature transition in SU(2) and SU(3) pure gauge theory in (2+1) dimensions. We also measure Wilson loops at $T=0$ on a wide range of $β$ values using APE smearing to improve the signal. We extract the string tension $σ$ from a fit to large distances, including a string fluctuation term. With these two entities we calculate $T_c/\sqrtσ$.

Figures (4)

• Figure 1: Susceptibility for $N_{\tau}=4$, SU(3)
• Figure 2: $\beta_{c, \infty}$ and $\gamma/\nu$ from the $\chi^2$ method
• Figure 3: Scaling behaviour of the string tension
• Figure 4: The cut-off dependence of $T_c/\sqrt{\sigma}$