The finite volume effects on the critical endpoint of chiral phase transition in Nambu–Jona-Lasinio model with different regularization schemes

Abstract

In this paper, we study the influence of different regularization schemes on the critical endpoint (CEP) of chiral phase transition within a cubic box with volume [Formula: see text]. A two-flavor Nambu–Jona-Lasinio model at finite temperature [Formula: see text] and chemical potential [Formula: see text] is adopted as the effective model of the strong interacting matter. Due to the finite volume of the box, the momentum integral in gap equation is replaced by discrete summation, and an anti-periodic boundary condition for quark field is applied. We employ the Schwinger’s proper time and the Pauli–Villars regularization (PVR) schemes, respectively. It is found that the first-order phase transition line displays an intriguing “staircase” behavior, and eventually disappears as [Formula: see text] increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit [Formula: see text]. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively.