发表机构
Technische Universität Wien（维也纳工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出自旋模型的双簇交换几何表示，证明Pfaffian关系蕴含平面性，并推广经典论证证明一类自旋模型相变的尖锐性，兼具理论意义与方法通用性。
AI 中文摘要
我们引入并研究了一般经典自旋模型的一种新几何表示，它由两个耦合的渗流构型构成，是自旋模型两个独立副本的Ginibre旋转的联合FK（随机簇）表示，可视为Sheffield在高度函数背景下定义的簇交换的推广。我们的方法结合了伊辛模型的随机电流与FK表示的优势：它为各类截断相关函数提供了渗流解释，同时满足FKG不等式（针对一大类模型）。我们通过建立两个截然不同的结果来凸显其优势与通用性：首先，我们证明了平面伊辛模型的边界多点相关函数由两点函数的Pfaffian给出这一经典事实的逆命题，即若一般图上的一般自旋模型满足Pfaffian关系，则在自然局部修正下，它必为平面图上的伊辛模型，特别地，代数Pfaffian关系蕴含平面性这一拓扑特征；其次，我们对Ellis、Monroe和Newman首次考虑的一类自旋模型，通过推广Duminil-Copin与Tassion的著名论证（用我们的新表示替代随机电流的使用），证明了其相变的尖锐性。
英文摘要
We introduce and study a new geometric representation for general classical spin models. It consists of two coupled percolation configurations that are the joint FK (random cluster) representation of the Ginibre rotation of two independent copies of the spin model, and can be viewed as an extension of Sheffield's cluster swapping defined in the context of height functions. Our approach combines the advantages of the random current and FK representations of the Ising model: it provides a percolation interpretation for various truncated correlation functions and at the same time satisfies the FKG inequality (for a large subclass of models). We highlight its strength and versatility by establishing two very different results. We first prove the converse of the classical fact that boundary multi-point correlation functions of planar Ising models are given by Pfaffians of the two-point functions. Indeed, we show that if a general spin model on a general graph satisfies the Pfaffian relations, then up to natural local modifications it must actually be an Ising model on a planar graph. In particular, the algebraic Pfaffian relations imply the topological feature of planarity. Our second application is a proof of sharpness of the phase transition for a class of spin models first considered by Ellis, Monroe and Newman, which we do by generalising the celebrated argument of Duminil-Copin and Tassion, replacing the use of the random current with our new representation.
Comments44 pages, 7 figures
