Monte Carlo simulations of the NJL model near the nonzero temperature phase transition

TL;DR

This paper uses Monte Carlo simulations to study the phase transition behavior of the NJL model at nonzero temperature, confirming its second order nature and universality class, with results consistent across different quark color numbers.

Contribution

It provides numerical evidence supporting the second order phase transition and universality class of the NJL model, including the suppression of the Ginzburg region with increasing N_c.

Findings

The NJL model undergoes a second order phase transition.

Critical exponents match the 3d O(4) universality class.

Ginzburg region shrinks as 1/N_c, aligning with analytical predictions.

Abstract

We present results from numerical simulations of the Nambu-Jona-Lasinio model with an SU(2)xSU(2) chiral symmetry and N_c=4,8, and 16 quark colors at nonzero temperature. We performed the simulations by utilizing the hybrid Monte Carlo and hybrid Molecular Dynamics algorithms. We show that the model undergoes a second order phase transition. The critical exponents measured are consistent with the classical 3d O(4) universality class and hence in accordance with the dimensional reduction scenario. We also show that the Ginzburg region is suppressed by a factor of 1/N_c in accordance with previous analytical predictions.