Toward an analytic determination of the deconfinement temperature in SU(2) L.G.T.

TL;DR

This paper analytically derives the deconfinement temperature in SU(2) lattice gauge theory at finite temperature, using character expansion and mean field methods, and validates results against Monte Carlo simulations.

Contribution

It provides an exact effective action for Polyakov loops in SU(2) gauge theory and determines the deconfinement transition point analytically, aligning well with numerical simulations.

Findings

Analytic expression for the deconfinement temperature

Good agreement with Monte Carlo results for N_t=1 to 5

Qualitative match with QCD scaling laws

Abstract

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings $\beta_t$ and $\beta_s$ for timelike and spacelike plaquettes. By using the character expansion of the Wilson action and performing the integrals over space-like link variables, we find an effective action for the Polyakov loops which is exact to all orders in $\beta_t$ and to the first non-trivial order in $\beta_s$. The critical coupling for the deconfinement transition is determined in the (3+1) dimensional case, by the mean field method, for different values of the lattice size $N_t$ in the compactified time direction and of the asymmetry parameter $\rho = \sqrt{\beta_t/\beta_s}$. We find good agreement with Montecarlo simulations in the range $1\leq N_t \leq 5$, and good qualitative agreement in the same range with the logarithmic scaling law of QCD. Moreover the dependence of the results from the parameter $\rho$ is in excellent agreement with previous theoretical predictions.