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The phase diagram of the two-dimensional Nambu--Jona-Lasinio model withisospin is explored in the large Nc limit with semiclassical methods. Weconsider finite temperature and include chemical potentials for all conservedcharges. In the chiral limit, a full analytical solution is presented,expressed in terms of known results for the single-flavor Gross-Neveu andNambu--Jona-Lasinio models. A novel crystalline structure appears and is shownexplicitly to be thermodynamically more stable than the homogeneous phase atzero temperature. If we include a bare fermion mass, the problem reduces againto solved problems in one-flavor models provided that either the fermionic orthe isospin chemical potentials vanish. In the general case, a stabilityanalysis is used to construct the perturbative phase boundary betweenhomogeneous and inhomogeneous phases. This is sufficient to get a good overviewof the complete phase diagram. Missing non-perturbative phase boundariesrequiring a full numerical Hartree-Fock calculation will be presented in futurework.

Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin