Title: Finite-size scaling of Lee-Yang zeros and its application to the 3-state Potts model and heavy-quark QCD Show Chinese title

Title: Lee-Yang零点的有限尺寸标度及其在三态Potts模型和重夸克QCD中的应用

Abstract: We propose a new general method to study critical points (CP) using the finite-size scaling of Lee-Yang zeros (LYZ). We first study the LYZ in the three-dimensional Ising model on finite lattices. We show that the ratios of multiple LYZ (Lee-Yang-zero ratios: LYZR) have useful scaling properties similar to the Binder cumulants, providing us with a novel method to study CP. In numerical simulations of the Ising model, we confirm that this method works well. We then apply the method to analyze the CP in the three-dimensional three-state Potts model and finite-temperature QCD in heavy-quark region, which are believed to belong to the same universality class as the Ising model. In these models, the partition function at complex parameters can be evaluated by the reweighting method, which allows us to determine the LYZ by varying coupling parameters continuously around the CP. We demonstrate that the LYZR method is powerful in determining the location of the CP in these models. Show Chinese abstract

Abstract: 我们提出了一种新的通用方法，利用李-杨零点（LYZ）的有限尺寸标度来研究临界点（CP）。 我们首先研究了有限格点上三维伊辛模型中的LYZ。 我们表明，多个LYZ的比值（李-杨零点比值：LYZR）具有类似于Binder累积量的有用标度性质，为我们提供了一种研究CP的新方法。 在伊辛模型的数值模拟中，我们确认了该方法效果良好。 随后，我们将该方法应用于分析三维三状态庞特模型和重夸克区域中的有限温度QCD的CP，这些模型被认为与伊辛模型属于同一普适类。 在这些模型中，可以通过重加权方法计算复参数下的配分函数，这使我们能够在CP附近连续改变耦合参数以确定LYZ。 我们证明，LYZR方法在确定这些模型中CP的位置方面非常有效。