  We generalize our previous model to an O(N) symmetric two-dimensional model
which possesses chiral symmetry breaking and superconducting (Cooper pair
condensates) phases at large-N. At zero temperature and density, the model can
be solved analytically in the large-N limit. We perform the renormalization
explicitly and obtain a closed form expression of the effective potential.
There exists a renormalization group invariant parameter $\delta$ that
determines which of the condensates exist in the vacuum. At finite temperatures
and densities, we map out the phase structure of the model by a detailed
numerical analysis of the renormalized effective potential. For $\delta$
positive and sufficiently large, the phase diagram in the $\mu$-$T$ (chemical
potential-temperature) plane exactly mimics the features expected for QCD with
two light flavors of quarks. At low temperatures there exists low-$\mu$ chiral
symmetry breaking and high-$\mu$ Cooper pair condensate regions which are
separated by a first-order phase transition. At high $\mu$, when the
temperature is raised, the system undergoes a second-order phase transition
from the superconducting phase to an unbroken phase in which both condensates
vanish. For a range of values of $\delta$ the theory possesses a tricritical
point ($\mu_{tc}$ and $T_{tc}$); for $\mu > \mu_{tc}$ ($\mu < \mu_{tc}$) the
phase transition from the low temperature chiral symmetry breaking phase to
unbroken phase is first-order (second-order). For the range of $\delta$ in
which the system mimics QCD, we expect the model to be useful for the
investigation of dynamical aspects of nonequilibrium phase transitions, and to
provide information relevant to the study of relativistic heavy ion collisions
and the dense interiors of neutron stars.
