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

The large-N limit of the two-dimensional U (N) (Wilson) lattice gauge theory is explicitly evaluated for all fixed =g^2N by steepest-descent methods. The dependence is discussed and a third-order phase transition, at =2, 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.