Location of zeros for the partition function of the Ising model on bounded degree graphs
Location of zeros for the partition function of the Ising model on bounded degree graphs
复制标题
DOI：
10.1112/jlms.12286
复制
发表时间：
2018-10
期刊：
影响因子：
--
通讯作者：
Han Peters;Guus Regts
中科院分区：
文献类型：
--
作者：
Han Peters;Guus Regts
开创性的Lee-Yang定理指出，对于任何图形，铁磁Ising模型的配分函数的零点位于C中的单位圆上。事实上，所有图的零的并集在单位圆上是密集的。在本文中，我们研究了在铁磁和反铁磁情况下，有界最大度d大于或等于3的图类的零的位置。我们将位置精确地确定为逆温度和度d的函数。我们方法中的一个重要步骤是转化为复杂动力学的设置，并分析与配分函数自然相关的动力系统。
The seminal Lee–Yang theorem states that for any graph the zeros of the partition function of the ferromagnetic Ising model lie on the unit circle in C . In fact, the union of the zeros of all graphs is dense on the unit circle. In this paper, we study the location of the zeros for the class of graphs of bounded maximum degree d⩾3 , both in the ferromagnetic and the anti‐ferromagnetic case. We determine the location exactly as a function of the inverse temperature and the degree d . An important step in our approach is to translate to the setting of complex dynamics and analyze a dynamical system that is naturally associated to the partition function.