Particle density in zero temperature symmetry restoring phase transitions in four-fermion interaction models

TL;DR

This paper analyzes particle density behavior at zero temperature in four-fermion models, revealing discontinuities and continuous transitions in density and its derivative across critical points, explaining phase transition types.

Contribution

It provides explicit calculations showing how particle density behaves at T=0 in various four-fermion models, clarifying the nature of phase transitions and the role of the tricritical point.

Findings

Particle density jumps discontinuously at first-order transitions in 2D and 3D GN models.

Density remains continuous but its derivative jumps at second-order transitions.

The results elucidate the physical implications of the tricritical point in the phase diagram.

Abstract

By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we have shown by explicit calculations that when T=0 the particle density will have a discontinuous jumping across the critical chemical potential $\mu_c$ in 2D and 3D Gross-Neveu (GN) model and these physically explain the first order feature of corresponding symmetry restoring phase transitions. For second order phase transitions in 3D GN model when $T\to 0$ and in 4D Nambu-Jona-Lasinio (NJL) model when T=0, it has been proven that the particle density itself will be continuous across $\mu_c$ but its derivative over the chemical potential $\mu$ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point $(T,\mu)=(0,\mu_c)$ in 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.