Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions

The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massless Gross-Neveu model in 2+1 dimensions. In the temperature and chemical potential plane, our results give strong support to the existence of a tricritical point and line of first order phase transition, previously only suspected to exist from extensive lattice Monte Carlo simulations. In addition of presenting these results we discuss how the OPT can be implemented in conjunction with the Landau expansion in order to determine all the relevant critical quantities.

Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model

A complete thermodynamical analysis of the 2+1 dimensional massless Gross-Neveu model is performed using the optimized perturbation theory. This is a non-perturbative method that allows us to go beyond the known large-N results already at lowest order. Our results, for a finite number of fermion species, N, show the existence of a tricritical point in the temperature and chemical potential phase diagram for discrete chiral phase transition allowing us to precisely to locate it. By studying the phase diagram in the pressure and inverse density plane, we also show the existence of a liquid-gas phase, which, so far, was unknown to exist in this model. Finally, we also derive N dependent analytical expressions for the fermionic mass, critical temperature and critical chemical potential.

The 2d Gross-Neveu Model at Finite Temperature and Density with Finite Corrections

We use the linear $delta$ expansion, or optimized perturbation theory, to evaluate the effective potential for the two dimensional Gross-Neveu model at finite temperature and density obtaining analytical equations for the critical temperature, chemical potential and fermionic mass which include finite $N$ corrections. Our results seem to improve over the traditional large-N predictions.