Abstract
The existence of crystalline condensates in the temperature and chemical potential phase diagram of the Gross-Neveu models can be traced to intricate symmetries of the associated inhomogeneous gap equation. The gap equation based on the Ginzburg-Landau expansion is precisely the mKdV or AKNS hierarchy of integrable nonlinear equations for the Gross-Neveu model with discrete or continuous chiral symmetry, respectively. The former model also has a dense-dilute symmetry that is due to the energy-reflection duality of the underlying quasi-exactly soluble spectral operators.
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