Anisotropic percolation and the d-dimensional surface roughening problem

Inhomogeneous anisotropic percolation: Two-dimensional numerical threshold analysis.

Surface critical phenomena in three-dimensional percolation.

Using Monte Carlo methods and finite-size scaling, we investigate surface critical phenomena in the bond-percolation model on the simple-cubic lattice with two open surfaces in one direction. We decompose the whole lattice into percolation clusters and sample the surface and bulk dimensionless ratios Q1 and Qb, defined on the basis of the moments of the cluster-size distribution. These ratios a...

Anisotropic bond percolation

We introduce anisotropic bond percolation in which there exist different occupation probabilities for bonds placed in different coordinate directions. We study in detail a d-dimensional hypercubical lattice, with probabilities p I for bonds within (d 1)-dimensional layers perpendicular to the z direction, and p11= Rp, for bonds parallel to z . For this model, we calculate low-density series for...

Site percolation and random walks on d-dimensional Kagomé lattices

The site percolation problem is studied on d-dimensional generalizations of the Kagomé lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q = 2d . The site percolation thresholds are calculated numerically for d = 3, 4, 5, and 6. The scaling of these thresholds as a function of dimension d, or alternatively q, is dif...

Model for Anisotropic Directed Percolation

We propose a simulation model to study the properties of directed percolation in two-dimensional (2D) anisotropic random media. The degree of anisotropy in the model is given by the ratio μ between the axes of a semiellipse enclosing the bonds that promote percolation in one direction. At percolation, this simple model shows that the average number of bonds per site in 2D is an invariant equal ...