Cardy和Schramm公式的推广

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-04-10 DOI:10.1007/s00220-025-05255-z

Mikhail Khristoforov, Mikhail Skopenkov, Stanislav Smirnov

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引用次数: 0

摘要

我们研究三角形网格上的临界点渗滤。我们找到了在两个给定点的右侧和左侧（即与界面相交的三角形的结合点不会将两点分开）出现渗滤界面的概率之差。这概括了卡迪公式和施拉姆公式。这一推广涉及一个新的有趣的离散分析观测值和一个意想不到的共形映射。

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A Generalization of Cardy’s and Schramm’s Formulae

We study critical site percolation on the triangular lattice. We find the difference of the probabilities of having a percolation interface to the right and to the left of two given points (such that the union of the triangles intersecting the interface does not separate the points) in the scaling limit. This generalizes both Cardy’s and Schramm’s formulae. The generalization involves a new interesting discrete analytic observable and an unexpected conformal mapping.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.