Work

Continuity of the phase transition for long-range Bernoulli percolation with exponential decay on $\mathbb{Z}^{2}$

Year: 2026

Type: preprint

Abstract: We prove continuity of the phase transition for long-range Bernoulli percolation on $\mathbb{Z}^{2}$ with connection probabilities that decay at least exponentially fast. This extends earlier work by Duminil-Copin, Sidoravicius, and Tassion on slabs. Our proof establishes a finite-size criterion that allows us to run a renormalisation argument. As a corollary, we obtain supercritical sharpness, in the sense that for every $β>β_c$, there exists a unique macroscopic cluster in large boxes with high probability.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.35233

Authors: Angel, Omer, de la Riva, Daniel, Panagiotis, Christoforos, Shi, Yuliang

Institutions: University of British Columbia, University of Bath

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Natural Sciences and Engineering Research Council of Canada, Engineering and Physical Sciences Research Council

Award: Large-scale universal behaviour of the Ising model

OpenAlex ID: W7223926703

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