Pfaffian Correlation Functions of Planar Dimer Covers

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• 作者：Michael Aizenman ; Manuel Laínz Valcázar ; Simone Warzel
• 刊名：Journal of Statistical Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：166
• 期：3-4
• 页码：1078-1091
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9613
• 卷排序：166

文摘

The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial/topological argument. These functions are then extended into a larger family of order–disorder correlation functions which are shown to exhibit Pfaffian structure throughout the bulk. Key tools involve combinatorial switching symmetries which are identified through the loop-gas representation of the double dimer model, and topological implications of planarity.