平面多边形马氏场的Dobrushin-Kotecky-Shlosman定理
Dobrushin-Kotecky-Shlosman theorem for polygonal Markov fields in the plane
摘要：
我们考虑所谓的长度相互作用的Arak-Surgailis多边形马尔可夫场与V形节点-一个连续和等距不变的过程中的平面共享的一些属性与二维伊辛模型。对于这些多边形的领域，我们建立了低温相分离定理的Dobrushin-Kotecky-Shlosman理论的精神，与相应的Wulff形状determined是一个磁盘，由于所考虑的模型的旋转不变性质。作为一个重要的工具，取代了经典的集群扩展技术，非常适合我们的几何设置，我们使用的是一个图形化的建设轮廓的出生和死亡的过程，以下的想法费尔南德斯，法拉利和加西亚。
英文摘要：
We consider the so-called length-interacting Arak-Surgailis polygonal Markov fields with V-shaped nodes - a continuum and isometry invariant process in the plane sharing a number of properties with the two-dimensional Ising model. For these polygonal fields we establish a low-temperature phase separation theorem in the spirit of the Dobrushin-Kotecky-Shlosman theory, with the corresponding Wulff shape deteremined to be a disk due to the rotation invariant nature of the considered model. As an important tool replacing the classical cluster expansion techniques and very well suited for our geometric setting we use a graphical construction built on contour birth and death process, following the ideas of Fernandez, Ferrari and Garcia.
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