Full Phase Diagram of the Massive Gross-Neveu Model

TL;DR

This paper provides a comprehensive analysis of the phase diagram of the massive Gross-Neveu model at finite temperature and chemical potential, revealing multiple phases and phase transitions with implications for condensed matter physics.

Contribution

It presents an exact solution of the model's phase diagram using Jacobi elliptic functions, including new phases and detailed phase boundary equations.

Findings

Identification of kink-antikink crystal and fermion gas phases.

All phase transitions are second order.

Generalization of bipolaron lattice to finite temperature.

Abstract

The massive Gross-Neveu model is solved in the large N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi elliptic functions. It contains three parameters which are determined by transcendental equations. Self-consistency of the scalar potential is proved. The phase diagram for non-zero bare quark mass is found to contain a kink-antikink crystal phase as well as a massive fermion gas phase featuring a cross-over from light to heavy effective fermion mass. For zero bare quark mass we recover the three known phases kink-antikink crystal, massless fermion gas, and massive fermion gas. All phase transitions are shown to be of second order. Equations for the phase boundaries are given and solved numerically. Implications on condensed matter physics are indicated where our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.