Critical analyses of order parameter and phase transitions at high density in Gross-Neveu model

TL;DR

This paper critically analyzes the order parameter and phase transitions at high density in the Gross-Neveu model, revealing the effectiveness of the gap equation in studying phase transitions and confirming the occurrence of a first order transition in D=3 at zero temperature.

Contribution

It demonstrates that the gap equation is as effective as effective potentials for analyzing phase transitions in the Gross-Neveu model and establishes the occurrence of a first order transition in D=3 at zero temperature.

Findings

The gap equation effectively analyzes phase transitions.

Confirmation of a first order phase transition in D=3 GN model at zero temperature.

Theoretical clarification of divergences in the analysis.

Abstract

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D=2 and D=3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some special first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D=3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.