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Cardy's formula for some dependent percolation models |
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| Authors: | F Camia C M Newman V Sidoravicius |
| Institution: | (1) Department of Physics, NewYork University, NewYork, NY 10003, USA E-mail: federico.camia@physics.nyu.edu, US;(2) Courant Inst. of Mathematical Sciences, NewYork University, NewYork, NY 10012, USA E-mail: newman@courant.nyu.edu, US;(3) Instituto de Matematica Pura e Aplicada, 22460-320 Rio de Janeiro, RJ BRAZIL E-mail: vladas@impa.br, BR |
| 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 (with alternating updates of two sublattices) 7]; 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. Received: 24 December 2001 |
| Keywords: | : Cardy's formula dependent percolation conformal invariance cellular automaton hexagonal lattice |
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