Variational study of the Gross-Neveu model

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Abstract
We study the Gross-Neveu model by using a variational method with an improved trial vacuum state. We obtain vacuum energies which are lower than the ones derived from the Gaussian approximation. The model is shown to have two phases. When the bare coupling constant is infinitesimal, the model exhibits spontaneous symmetry breaking. For a finite bare coupling constant, it is in another phase where symmetry does not break spontaneously. We compare our results with those of the large-N approximation.