Universal crossing probabilities and incipient spanning clusters in directed percolation

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dc.creatorTurban, L.
dc.date2003-02-10
dc.date2003-06-23
dc.date.accessioned2026-07-07T02:49:37Z
dc.date.available2026-07-07T02:49:37Z
dc.descriptionShape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. Since the system is strongly anisotropic, the shape-dependence enters through the effective aspect ratio r_eff=cL^z/t, where c is a non-universal constant and z the anisotropy exponent. A particular attention is paid to the influence of the initial state on the universal behaviour of the crossing probability. Using anisotropic finite-size scaling and generalizing a simple argument given by Aizenman for isotropic percolation, we obtain the behaviour of the probability to find n incipient spanning clusters on a finite system at time t. The numerical results are in good agreement with the conjecture.
dc.description8 pages, 12 figures; minor corrections
dc.identifierhttps://arxiv.org/abs/cond-mat/0302181
dc.identifierhttp://arxiv.org/abs/cond-mat/0302181
dc.identifierEur. Phys. J. B33 (2003) 331-338
dc.identifierdoi:10.1140/epjb/e2003-00173-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/20865
dc.subjectStatistical Mechanics
dc.titleUniversal crossing probabilities and incipient spanning clusters in directed percolation
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