论文标题
Lee-Yang的Curie-Weiss模型理论及其罕见波动
Lee-Yang theory of the Curie-Weiss model and its rare fluctuations
论文作者
论文摘要
相变通常伴随着自由能的非分析行为，可以通过考虑控制参数的复杂平面中分区函数的零以及它们对系统大小的临界值的方法来解释。最近的实验表明，分区函数零不仅是理论概念。还可以通过测量有限大小系统中热力学可观察物的波动来实验确定它们。在此进步的激励下，我们在这里研究了使用我们最近建立的累积方法的自发磁化模型的分区函数零。具体而言，我们从能量的波动和有限尺寸系统中的磁化物中提取了居里 - 韦斯模型的领先的渔民和李杨零。我们对分区函数零的有限尺寸缩放分析进行了有效的缩放分析，该分区零对平均场模型有效，这使我们能够提取控制参数的关键值和关键指数的关键值，即使对于远离关键性的小型系统也是如此。我们还表明，Lee-Yang Zeros具有有关罕见磁波动的重要信息，因为它们使我们能够预测磁化强度统计的许多基本特征。这一发现可能构成Lee-Yang理论与大差异统计数据之间的紧密联系。
Phase transitions are typically accompanied by non-analytic behaviors of the free energy, which can be explained by considering the zeros of the partition function in the complex plane of the control parameter and their approach to the critical value on the real-axis as the system size is increased. Recent experiments have shown that partition function zeros are not just a theoretical concept. They can also be determined experimentally by measuring fluctuations of thermodynamic observables in systems of finite size. Motivated by this progress, we investigate here the partition function zeros for the Curie-Weiss model of spontaneous magnetization using our recently established cumulant method. Specifically, we extract the leading Fisher and Lee-Yang zeros of the Curie-Weiss model from the fluctuations of the energy and the magnetization in systems of finite size. We develop a finite-size scaling analysis of the partition function zeros, which is valid for mean-field models, and which allows us to extract both the critical values of the control parameters and the critical exponents, even for small systems that are away from criticality. We also show that the Lee-Yang zeros carry important information about the rare magnetic fluctuations as they allow us to predict many essential features of the large-deviation statistics of the magnetization. This finding may constitute a profound connection between Lee-Yang theory and large-deviation statistics.
