发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将尺度归纳方案应用于s-嵌入上的FK-Ising模型，在一致有界几何假设下证明强RSW估计，该结果可用于近临界Ising模型等场景。
AI 中文摘要
我们将Duminil-Copin、Manolescu和Tassion的“尺度归纳”方案应用于s-嵌入上的FK-Ising模型。具体而言，在构成s-嵌入的切向四边形满足“一致有界几何”假设（所有边长与1可比，所有角度有下界）的条件下，我们证明了具有不利边界条件的粗糙拓扑四边形的穿越存在性，即所谓的“强”RSW。该结果有一系列标准推论，如臂事件的拟乘法性和团簇的分形性质。它可应用于多种场景，包括通过考虑正则网格上近临界Ising模型的适当s-嵌入，将其应用于关联长度尺度以下的情况。
英文摘要
We adapt the 'induction over scales' scheme of Duminil-Copin, Manolescu, and Tassion to the FK-Ising model on s-embeddings. Namely, we prove the existence of crossings of rough topological quadrilaterals with unfavorable boundary conditions, known as 'strong' RSW, under the 'uniformly bounded geometry' assumption (all edge lengths are comparable to 1 and all angles are bounded from below) on the tangential quads that form an s-embedding. This result has a number of standard consequences like quasi-multiplicativity of arm events and fractal properties of the clusters. It can be applied in a variety of setups including near-critical Ising models on regular grids below the correlation length scale by considering appropriate s-embedding thereof.
Comments34 pages, 5 figures
