  We explore the phase diagram of strongly interacting matter as a function of
temperature and baryon number density, using a class of models for two-flavor
QCD in which the interaction between quarks is modelled by that induced by
instantons. Our treatment allows us to investigate the possible simultaneous
formation of condensates in the conventional quark--anti-quark channel
(breaking chiral symmetry) and in a quark--quark channel leading to color
superconductivity: the spontaneous breaking of color symmetry via the formation
of quark Cooper pairs. At low temperatures, chiral symmetry restoration occurs
via a first order transition between a phase with low (or zero) baryon density
and a high density color superconducting phase. We find color superconductivity
in the high density phase for temperatures less than of order tens to 100 MeV,
and find coexisting $<qq>$ and $<\bar q q>$ condensates in this phase in the
presence of a current quark mass. At high temperatures, the chiral phase
transition is second order in the chiral limit and is a smooth crossover for
nonzero current quark mass. A tricritical point separates the first order
transition at high densities from the second order transition at high
temperatures. In the presence of a current quark mass this tricritical point
becomes a second order phase transition with Ising model exponents, suggesting
that a long correlation length may develop in heavy ion collisions in which the
phase transition is traversed at the appropriate density.
