Temperature induced phase transitions in four fermion models in curved space-time

TL;DR

This paper investigates how constant curvature space-time affects phase transitions in four-fermion models, specifically the Gross-Neveu model, at various temperatures and coupling strengths, revealing critical surfaces and symmetry-breaking behavior.

Contribution

It analytically determines the critical surface for phase transitions in the Gross-Neveu model on curved manifolds using zeta-function regularization, extending understanding of curvature effects.

Findings

Critical surfaces for phase transitions are analytically derived.

Symmetry is always broken at zero temperature in negative curvature.

Mass gap and free energy density are computed at criticality.

Abstract

The large N limit of the Gross-Neveu model is here studied on manifolds with constant curvature, at zero and finite temperature. Using the zeta-function regularization, the phase structure is investigated for arbitrary values of the coupling constant. The critical surface where the second order phase transition takes place is analytically found for both the positive and negative curvature cases. For negative curvature, where the symmetry is always broken at zero temperature, the mass gap is calculated. The free energy density is evaluated at criticality and the zero curvature and zero temperature limits are discussed.