Analytic results in 2+1-dimensional Finite Temperature LGT

Details Analytic results in 2+1-dimensional Finite Temperature LGT Analytic results in 2+1-dimensional Finite Temperature LGT

1997-01-27

arxiv.org/abs/hep-th/9701145v1

Int.J.Mod.Phys. A12 (1997) 5753-5766

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Latex, 2 figures included with epsf

Scientific paper

10.1142/S0217751X97003017

In a 2+1-dimensional pure LGT at finite temperature the critical coupling for the deconfinement transition scales as $\beta_c(n_t) = J_c n_t + a_1$, where $n_t$ is the number of links in the ``time-like'' direction of the symmetric lattice. We study the effective action for the Polyakov loop obtained by neglecting the space-like plaquettes, and we are able to compute analytically in this context the coefficient $a_1$ for any SU(N) gauge group; the value of $J_c$ is instead obtained from the effective action by means of (improved) mean field techniques. Both coefficients have already been calculated in the large N limit in a previous paper. The results are in very good agreement with the existing Monte Carlo simulations. This fact supports the conjecture that, in the 2+1-dimensional theory, space-like plaquettes have little influence on the dynamics of the Polyakov loops in the deconfined phase.

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