Nambu Jona Lasinio model with proper time regularization in a finite volume

Abstract: Based on the two flavor NJL model with a proper time regularization, we used stationary wave condition (SWC) for the first time to study the influence of the finite volume effects on the chiral phase transition of quark matter at finite temperature. It is found that when the cubic volume size L is large than LSWC = 500 fm, the chiral quark condensate is indistinguishable from that max at L = $\infinity$,Here it should be noted that 500 fm is far greater than the size of QGP produced at laboratory and the lattice QCD simulation space size. It is also much larger than the previous limit size LAPBC = 5 fm estimated by the commonly used anti-periodic boundary condition (APBC). max We also found that when the space size L is less than LSWC = 0.25 fm, the spontaneous symmetry min breaking concept is no longer valid. In addition, we first introduce the spatial susceptibility, and through the study of the spatial susceptibility, it was revealed for the first time that the chiral phase transition caused by the finite volume effects in the nonchiral limit is a crossover.