Percolation phase transition on planar spin systems

Caio Alves; Gideon Amir; Rangel Baldasso; Augusto Teixeira

doi:10.1214/23-aihp1410

Percolation phase transition on planar spin systems

Caio Alves, Gideon Amir, Rangel Baldasso, Augusto Teixeira

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this article we study the continuity and sharpness of the phase transition for percolation models defined on top of planar spin systems. The two examples that we treat in detail concern the Glauber dynamics for the Ising model and a Dynamic Bootstrap process. For both of these models we prove that their phase transition is continuous and sharp, providing also quantitative estimates on the two point connectivity. The techniques that we develop in this work can be applied to a variety of different percolation models based on spin-flip dynamics. We also discuss some of the problems that can be tackled in a similar fashion.

Original language	English
Pages (from-to)	2549-2580
Number of pages	32
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	60
Issue number	4
DOIs	https://doi.org/10.1214/23-aihp1410
State	Published - Nov 2024

Bibliographical note

Publisher Copyright:
© Association des Publications de l’Institut Henri Poincaré, 2024.

Keywords

Dependence
Percolation
Spin systems

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AU - Baldasso, Rangel

AU - Teixeira, Augusto

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PY - 2024/11

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N2 - In this article we study the continuity and sharpness of the phase transition for percolation models defined on top of planar spin systems. The two examples that we treat in detail concern the Glauber dynamics for the Ising model and a Dynamic Bootstrap process. For both of these models we prove that their phase transition is continuous and sharp, providing also quantitative estimates on the two point connectivity. The techniques that we develop in this work can be applied to a variety of different percolation models based on spin-flip dynamics. We also discuss some of the problems that can be tackled in a similar fashion.

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Percolation phase transition on planar spin systems

Abstract

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