This article gives an explicit formula for the leading term of the free energy of three-dimensional U(N) lattice gauge theory for any N, as the lattice spacing tends to zero. The proof is based on a novel technique that avoids phase cell renormalization. The technique also yields a similar formula for the four-dimensional theory, but only in the weak coupling~limit.
@article{arxiv.1602.01222,
title = {The leading term of the Yang-Mills free energy},
author = {Sourav Chatterjee},
journal= {arXiv preprint arXiv:1602.01222},
year = {2016}
}