Finite Density Effect in the Gross-Neveu Model in a Weakly Curved R¹times S² Spacetime

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.