The Four-Fermi Model in Three Dimensions at Non-Zero Density and Temperature

TL;DR

This study investigates the phase transition behavior of the three-dimensional four-Fermi model at finite density and temperature using Monte Carlo simulations, confirming analytic predictions and mapping the phase diagram.

Contribution

It provides the first non-zero density and temperature lattice study of the 3D four-Fermi model with large Nf, confirming analytic results and exploring finite size and mass effects.

Findings

First order chiral transition at zero temperature with critical chemical potential

Critical index of correlation length matches analytic calculations

Phase diagram mapped out with finite size and mass effects analyzed

Abstract

The Four Fermi model with discrete chiral symmetry is studied in three dimensions at non-zero chemical potential and temperature using the Hybrid Monte Carlo algorithm. The number of fermion flavors is chosen large $(N_f=12)$ to compare with analytic results. A first order chiral symmetry restoring transition is found at zero temperature with a critical chemical potential $\mu_c$ in good agreement with the large $N_f$ calculations. The critical index $\nu$ of the correlation length is measured in good agreement with analytic calculations. The two dimensional phase diagram (chemical potential vs. temperature) is mapped out quantitatively. Finite size effects on relatively small lattices and non-zero fermion mass effects are seen to smooth out the chiral transition dramatically.