  In this note we summarize the results from a longer article on obtaining the
QCD phase diagram as a function of the temperature and chemical potential at
large Nc and large Nf in the weak and the strong coupling limits. The weak
coupling phase diagram is obtained from the Polyakov line order parameter, and
the quark number, calculated using 1-loop perturbation theory for QCD
formulated on S^1 x S^3. The strong coupling phase diagram is obtained from the
same observables calculated at leading order in the lattice strong coupling and
hopping parameter expansions. We show that the matrix models in these two
limits agree at temperatures and chemical potentials which are not too high,
such that observables in the strongly-coupled theory can be obtained from the
observables in the weakly-coupled theory, and vice versa, using a simple
transformation of variables.
