Chiral symmetry restoration in the three-dimensional four-fermion model at non-zero temperature and density

Abstract

The phase structure of the three-dimensional four-fermion model with a Z2 chiral symmetry at non-zero temperature Tor non-zero chemical potential μ is investigated. The main purpose of the study is to serve as an orientation for the more complex problem of the chiral phase transition in Quantum Chromodynamics. It is shown that the critical properties near the finite temperature and zero density transition with a large number of fermion species N in the system can be described by mean field theory. It is also shown both analytically and numerically that the width of the region where non-trivial critical behavior sets in is suppressed by a certain power of 1/ N. At finite N, Monte Carlo simulations confirm the dimensional reduction scenario, which predicts the two-dimensional Ising universality class for the finite temperature transition. Analytical predictions based on the leading order of the 1/N expansion at zero temperature and non-zero chemical potential predict a first order transition. Monte Carlo simulations with N = 4 confirm the first order nature of the T = 0 transition. Some lessons are drawn relevant to lattice QCD simulations at non-zero T or non-zero μ.