  The phase diagram of the two-dimensional Nambu--Jona-Lasinio model with
isospin is explored in the large Nc limit with semiclassical methods. We
consider finite temperature and include chemical potentials for all conserved
charges. In the chiral limit, a full analytical solution is presented,
expressed in terms of known results for the single-flavor Gross-Neveu and
Nambu--Jona-Lasinio models. A novel crystalline structure appears and is shown
explicitly to be thermodynamically more stable than the homogeneous phase at
zero temperature. If we include a bare fermion mass, the problem reduces again
to solved problems in one-flavor models provided that either the fermionic or
the isospin chemical potentials vanish. In the general case, a stability
analysis is used to construct the perturbative phase boundary between
homogeneous and inhomogeneous phases. This is sufficient to get a good overview
of the complete phase diagram. Missing non-perturbative phase boundaries
requiring a full numerical Hartree-Fock calculation will be presented in future
work.
