Cardy's Formula for some Dependent Percolation Models

Details Cardy's Formula for some Dependent Percolation Models Cardy's Formula for some Dependent Percolation Models

2001-11-15

arxiv.org/abs/cond-mat/0111293v1

Physics

Condensed Matter

Statistical Mechanics

9 pages

Scientific paper

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.

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