We propose a novel edge-type strong spatial mixing (edge-SSM) property for ferromagnetic Ising models on arbitrary graphs, and establish its validity across the complete Lee-Yang zero-free region. Furthermore, we demonstrate that this edge-SSM property induces a standard form of SSM in the corresponding random cluster model, thereby generalizing previous lattice-specific SSM results to arbitrary graph structures.

Our technical approach leverages Regts' framework through the development of an innovative division relation method, which enables us to establish local dependence of coefficients. Notably, this division relation paradigm exhibits universal applicability across diverse statistical mechanical systems, including Potts models, hypergraph independence polynomials, and Holant-type partition functions. For each system, we establish previously unknown SSM properties directly from their respective zero-free regions, thus revealing a profound correspondence between complex zeros of the partition function and correlation decay.

Based on joint work with Ke Shi.

邵帅，中国科学技术大学计算机学院特任教授。2014年本科毕业于中国科大少年班学院华罗庚班，2020年博士毕业于威斯康星大学麦迪逊分校计算机系，之后分别在牛津大学及爱丁堡大学从事博士后工作。研究领域为理论计算机科学，主要研究方向为Edge-CSP框架下判定、优化及计数问题（即Holant问题）的计算复杂性分类，同时涉及其与统计物理中相变概念以及量⼦纠缠理论的交叉问题。