We compute the expansion of the 3-d Lattice Yang-Mills free energy to four-loop order by means of Numerical Stochastic Perturbation Theory. The ﬁrst and second order are already known and are correctly reproduced. The third- and fourth-order coeﬃcients are new results. The known logarithmic divergence in the fourth order is correctly identiﬁed. We comment on the relevance of our computation in the context of dimensionally reduced ﬁnite temperature QCD.
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