2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185626The 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.RevTeX, minor changes, new references are addedHigh Energy Physics - TheoryHigh Energy Physics - Phenomenologytext