  In this paper we continue our study of the thermodynamics of large N gauge
theories on compact spaces. We consider toroidal compactifications of pure
SU(N) Yang-Mills theories and of maximally supersymmetric Yang-Mills theories
dimensionally reduced to 0+1 or 1+1 dimensions, and generalizations of such
theories where the adjoint fields are massive. We describe the phase structure
of these theories as a function of the gauge coupling, the geometry of the
compact space and the mass parameters. In particular, we study the behavior of
order parameters associated with the holonomy of the gauge field around the
cycles of the torus. Our methods combine analytic analysis, numerical Monte
Carlo simulations, and (in the maximally supersymmetric case) information from
the dual gravitational theories.
