  We review and extend earlier work that uses the AdS/CFT correspondence to
relate the black hole-black string transition of gravitational theories on a
circle to a phase transition in maximally supersymmetric 1+1-dimensional SU(N)
gauge theories at large N, again compactified on a circle. We perform gravity
calculations to determine a likely phase diagram for the strongly coupled gauge
theory. We then directly study the phase structure of the same gauge theory,
now at weak 't Hooft coupling. In the interesting temperature regime for the
phase transition, we may reduce the 1+1-dimensional theory to a 0+1-dimensional
bosonic theory, which we solve using Monte Carlo methods. We find strong
evidence that the weakly coupled gauge theory also exhibits a black hole-black
string like phase transition in the large N limit. We demonstrate that a simple
Landau-Ginzburg like model describes the behaviour near the phase transition
remarkably well. The weak coupling transition appears to be close to the cusp
between a first order and a second order transition.
