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

Abstract

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings $β_t$ and $β_s$ 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 $β_t$ and to the first non-trivial order in $β_s$. 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 $ρ= \sqrt{β_t/β_s}$. 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 $ρ$ is in excellent agreement with previous theoretical predictions.