  We study the deconfining phase transition at nonzero temperature in a SU(N)
gauge theory, using a matrix model which was analyzed previously at small N. We
show that the model is soluble at infinite N, and exhibits a Gross-Witten-Wadia
transition. In some ways, the deconfining phase transition is of first order:
at a temperature $T_d$, the Polyakov loop jumps discontinuously from 0 to1/2,
and there is a nonzero latent heat $\sim N^2$. In other ways, the transition is
of second order: e.g., the specific heat diverges as $C \sim 1/(T-T_d)^{3/5}$
when $T \rightarrow T_d^+$. Other critical exponents satisfy the usual scaling
relations of a second order phase transition. In the presence of a nonzero
background field $h$ for the Polyakov loop, there is a phase transition at the
temperature $T_h$ where the value of the loop =1/2, with $T_h < T_d$. Since
$\partial C/\partial T \sim 1/(T-T_h)^{1/2}$ as $T \rightarrow T_h^+$, this
transition is of third order.
