Numerical results for crossing, spanning and wrapping in two-dimensional percolation
نویسندگان
چکیده
Using a recently developed method to simulate percolation on large clusters of distributed machines [1], we have numerically calculated crossing, spanning and wrapping probabilities in two-dimensional site and bond percolation with exceptional accuracy. Our results are fully consistent with predictions from Conformal Field Theory. We present many new results that await theoretical explanation, particularly for wrapping clusters on a cylinder. We therefore provide possibly the most up-to-date reference for theoreticians working on crossing, spanning and wrapping probabilities in two-dimensional percolation. Submitted to: J. Phys. A: Math. Gen. PACS numbers: 64.60.Ak, 05.70.Jk Crossing, spanning and wrapping in two-dimensional percolation 2
منابع مشابه
ساختار خوشههای پرکولاسیون تهاجمی در دو بعد
We have performed extensive numerical simulations to estimate the fractal dimension of the mass and also the anisotropy in the shape of sample spanning cluster (SSC) in 2-D site invasion percolation processes with and without trapping. In agreement with the most recent works, we have observed that these two different processes belong to two different universality classes. Furthermore, we have...
متن کاملUniversal crossing probabilities and incipient spanning clusters in directed percolation
Shape-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. In a dynamical interpretation, the crossing probability is the probability that, on a system with size L, an epidemic spreading without immunization remains active at time t. Since the sys...
متن کاملThe density of critical percolation clusters touching the boundaries of strips and squares
We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, halfinfinite strips and squares, as well as several related quantities for the infinite strip. Our theoretical results follow from conformal field theory and are compared with high-precision numerical simulation. For example, we show that the density of clus...
متن کاملA crossing probability for critical percolation in two dimensions
Langlands et al. considered two crossing probabilities, π h and π hv , in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of π h by treating it as a correlation function of boundary operators in the Q → 1 limit of the Q state Potts model. We extend his results to find an analogous formula for π hv which compares very well...
متن کاملIncipient Spanning Clusters in Square and Cubic Percolation
The analysis of extensive numerical data for the percolation probabilities of incipient spanning clusters in two dimensional percolation at criticality are presented. We developed an effective code for the single-scan version of the Hoshen-Kopelman algorithm. We measured the probabilities on the square lattice forming samples of rectangular strips with widths from 8 to 256 sites and lengths up ...
متن کامل