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

TL;DR

This paper investigates how finite particle density and weak curvature in a three-dimensional Gross-Neveu model influence phase transitions, deriving critical conditions for chiral symmetry breaking and restoration.

Contribution

It introduces an analysis of the Gross-Neveu model on a curved spacetime with finite density, deriving critical parameters for phase transitions involving curvature and chemical potential.

Findings

Identifies critical values of curvature and chemical potential for phase transition.

Derives an effective potential incorporating curvature and density effects.

Shows first order phase transition between broken and symmetric phases.

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.