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) [7]; it may also be realized on the triangular lattice double-struck T sign with flips when a site disagrees with six, five and sometimes four of its six neighbors.
Original language | English (US) |
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Pages (from-to) | 147-156 |
Number of pages | 10 |
Journal | Bulletin of the Brazilian Mathematical Society |
Volume | 33 |
Issue number | 2 |
DOIs | |
State | Published - Jul 2002 |
Keywords
- Cardy's formula
- Cellular automaton
- Conformal invariance
- Dependent percolation
- Hexagonal lattice
ASJC Scopus subject areas
- Mathematics(all)