Free energy and plaquette expectation value for gluons on the lattice, in three dimensions

We calculate the perturbative value of the free energy in lattice QCD in three dimensions, up to three loops. Our calculation is performed using the Wilson formulation for gluons in $SU(N)$ gauge theories. The free energy is directly related to the average plaquette. To carry out the calculation, we compute the coefficients involved in the perturbative expansion of the Free Energy up to three loops, using an automated set of procedures developed by us in Mathematica. The dependence on $N$ is shown explicitly in our results. For purposes of comparison, we also present the individual contributions from every diagram. These have been obtained by means of two independent calculations, in order to cross check our results.