Strong coupling phase in lattice gauge theories at large dimension

We study lattice gauge theories at large space-time dimension D. In the strong coupling (high-temperature) phase, the appropriate expansion parameter is D^{- 1 4}. We find that this phase, which becomes metastable at a certain temperature, is limited by a singular point which looks like a second-order phase transition. For the Z₂ gauge group, this happens at D tanh⁴β = 128 3125. At this temperature, the correlation length of two plaquettes becomes infinite. At D = ∞, the same result holds for any gauge group, only the value at which the transition occurs depends on the group. The corrections of orders D^{- 1 4} are different for different gauge groups. It is not yet clear to us if the Wilson loop changes its behaviour when the plaquette-plaquette correlation function does.