Percolation phase transition on planar spin systems

Annales de l Institut Henri Poincaré Probabilités et Statistiques, vol. 60

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.

Authors 4

1. Caio Alves

   Oak Ridge National Laboratory

   Affiliation as printed

   Oak Ridge National Laboratory, Knoxville, United States

2. Gideon Amir

   Bar-Ilan University

   Affiliation as printed

   Bar-Ilan University, 5290002, Ramat Gan, Israel

3. Rangel Baldasso Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

4. Augusto Teixeira

   Instituto Nacional de Matemática Pura e Aplicada

   Affiliation as printed

   IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ – Brazil