  We analyze in detail a second order phase transition that occurs in large N
Gaussian multi-matrix models in which the matrices are constrained to be
commuting. The phase transition occurs as the relative masses of the matrices
are varied, assuming that there are at least four matrices in the lowest mass
level. We also discuss the phase structure of weakly coupled large N 3+1
dimensional gauge theories compactified on a three-sphere of radius R. We argue
that these theories are well described at high temperatures (T >> 1/R) by a
Gaussian multi-matrix model, and that they do not exhibit any phase transitions
between the deconfinement scale (T ~ 1/R) and the scale where perturbation
theory breaks down (T ~ 1 / \lambda R, where \lambda is the 't Hooft coupling).
