Possible third-order phase transition in the large-Nlattice gauge theory

Abstract

The large-$N$ limit of the two-dimensional $\mathrm{U}\mathrm{}\left(N\right)\mathrm{}$ (Wilson) lattice gauge theory is explicitly evaluated for all fixed $\lambda =g^{2}N$ by steepest-descent methods. The $\lambda$ dependence is discussed and a third-order phase transition, at $\lambda =2\mathrm{}$, is discovered. The possible existence of such a weak- to strong-coupling third-order phase transition in the large-$N$ four-dimensional lattice gauge theory is suggested, and its meaning and implications are discussed.