Analytic results in 2+1-dimensional Finite Temperature LGT

TL;DR

This paper analytically investigates the critical coupling for deconfinement in 2+1D finite temperature lattice gauge theory, finding results that align well with Monte Carlo simulations and suggesting space-like plaquettes have limited impact.

Contribution

It provides an analytical computation of the effective action coefficients for the Polyakov loop in 2+1D LGT, extending previous large N results to finite N and confirming their accuracy.

Findings

Analytical expressions for critical coupling coefficients match Monte Carlo data.

Space-like plaquettes have minimal effect on Polyakov loop dynamics.

Supports the validity of simplified models neglecting space-like plaquettes.

Abstract

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.