Abstract
The phase structure of the two-dimensional Gross-Neveu model in a spacetime of the form R 1×S 1 and in the presence of a chemical potential µ is investigated. The phase portrait of the model is constructed in the parameter plane (µ, γ), where γ=1/L and L is the length of the circle S 1. In the portrait there exist two massive phases, with spontaneously broken chiral invariance, as well as infinitely many massless symmetric phases. Such a vacuum structure leads to oscillations of the critical curve µ c (γ) of chiral phase transitions. In addition, the particle number density in the vacuum state of the model oscillates if µ<µ c (γl).
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