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 $σ(x)$, which is expressed in terms of a scalar curvature $R$ and nonzero chemical potential $μ$. We then derive the critical values of $(R,μ)$ at which the system undergoes the first order phase transition from the phase with broken chiral invariance to the symmetric phase.