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 $V\sim L^3$. A two-flavor Nambu–Jona-Lasinio model at finite temperature $T$ and chemical potential $\mu$ 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 $T$ increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit $V\to \infty$. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively.

在本文中，我们研究了不同正则化方案对体积立方盒内手性相变临界端点（CEP）的影响$V～L^3$。有限温度下的两种风味 Nambu–Jona-Lasinio 模型$\mathrm{时间}$和化学势$\mu$采用作为强相互作用物质的有效模型。由于盒子体积有限，用离散求和代替间隙方程中的动量积分，并应用夸克场的反周期边界条件。我们分别采用 Schwinger 固有时间和 Pauli-Villars 正则化 (PVR) 方案。研究发现，一阶相变线表现出有趣的“阶梯”行为，并最终消失$\mathrm{时间}$增加。特别是，在无限体积限制下，两种正则化方案都不存在 CEP$V\to \mathrm{无穷大}$。然而，对于有限体积，具有适当时间和PVR的CEP的位置是分别确定的。