Finite Density Effect in the Gross-Neveu Model in a Weakly Curved $R^1\times S^2$ Spacetime

Abstract

The three-dimensional Gross-Neveu model in $R^1\times S^2$ spacetime is considered at finite particles number density. We evaluate an effective potential of the composite scalar field $\sigma (x)$, which is expressed in terms of a scalar curvature $R$ and nonzero chemical potential $\mu$. We then derive the critical values of $(R,\mu )$ at which the system undergoes the first order phase transition from the phase with broken chiral invariance to the symmetric phase.

Comments: RevTeX, minor changes, new references are added