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

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

1996-01-29

arxiv.org/abs/hep-lat/9601020v1

Nucl.Phys. B472 (1996) 163-193

Physics

High Energy Physics

High Energy Physics - Lattice

uuencoded latex file of 32 pages plus 3 ps figures

Scientific paper

10.1016/0550-3213(96)00223-4

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.

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