2017/10/29 by Vincent Beffara, Beffara, Vincent, Damien Gayet +1 · 1 citation
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.1710.10644
We prove a Russo-Seymour-Welsh theorem for the antiferromagnetic Ising model with small parameter on a regular enough periodic planar triangulation. More generally we prove that the box-crossing property extends to a neighborhood of the product measure among certain families of discrete percolation models that do not necessarily satisfy the Fortuin-Kasteleyn-Ginibre condition of positive association.