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Recent numerical calculations have shown that the ground state of the Gross-Neveu model at finite density is a crystal. Here, we present the analytical solution of this problem in terms of elliptic functions. The scalar potential is the superpotential of the nonrelativistic Lam\'e Hamiltonian. This model can also serve as an analytically solvable toy model for a relativistic superconductor in the Larkin-Ovchinnikov-Fulde-Ferrell phase.
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Michael Thies (2004) studied this question.
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