Cardy's Formula for some Dependent Percolation Models
Statistical Mechanics
2007-05-23 v1 Probability
Abstract
We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice H (with alternating updates of two sublattices); it may also be realized on the triangular lattice T with flips when a site disagrees with six, five and sometimes four of its six neighbors.
Cite
@article{arxiv.cond-mat/0111293,
title = {Cardy's Formula for some Dependent Percolation Models},
author = {Federico Camia and Charles M. Newman and Vladas Sidoravicius},
journal= {arXiv preprint arXiv:cond-mat/0111293},
year = {2007}
}
Comments
9 pages