Inhomogeneous condensates in the thermodynamics of the chiral NJL2 model

We analyze the thermodynamical properties, at finite density and nonzero temperature, of the (1+1) dimensional chiral Gross-Neveu model (the NJL(2) model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the chiral spiral, as a thermodynamically preferred limit of the more general twisted kink crystal solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a discrete chiral symmetry, and for which the phase diagram has a crystalline phase with a periodic kink crystal. We use a combination of analytic, numerical, and Ginzburg-Landau techniques to study various parts of the phase diagram.