Related papers: Bond and Site Percolation in Three Dimensions
We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced…
By means of Monte Carlo simulations, we study long-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors, up to the eighth neighbors for the square lattice and the ninth neighbors for the…
The site percolation thresholds p_c are determined to high precision for eight Archimedean lattices, by the hull-walk gradient-percolation simulation technique, with the results p_c = 0.697043, honeycomb or (6^3), 0.807904 (3,12^{2}),…
We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point…
We have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices. For the square bond problem we have extended the series from 41 terms to 54, for the square site…
I construct a two-dimensional lattice on which the inhomogeneous site percolation threshold is exactly calculable and use this result to find two more lattices on which the site thresholds can be determined. The primary lattice studied…
Extensive Monte-Carlo simulations were performed in order to determine the precise values of the critical thresholds for site ($p^{hcp}_{c,S} = 0.199 255 5 \pm 0.000 001 0$) and bond ($p^{hcp}_{c,B} = 0.120 164 0 \pm 0.000 001 0$)…
We use a new algorithm to find the stress-carrying backbone of ``generic'' site-diluted triangular lattices of up to 10^6 sites. Generic lattices can be made by randomly displacing the sites of a regular lattice. The percolation threshold…
We investigate site and bond percolation in triangular and square lattices subjected to linear distortion. In contrast to previously studied distortion schemes that preserve lattice geometry, linear distortion dislocates regular lattice…
In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network. The characteristic properties of percolation is that it…
The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we…
We study site- and bond-percolation on a class of lattices referred to as Lieb lattices. In two dimensions the Lieb lattice (LL) is also known as the decorated square lattice, or as the CuO$_2$ lattice; in three dimensions it can be…
A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices…
We extend the method of Balister, Bollob\'as and Walters for determining rigorous confidence intervals for the critical threshold of two dimensional lattices to three (and higher) dimensional lattices. We describe a method for determining a…
The site and bond percolation problems are conventionally studied on (hyper)cubic lattices, which afford straightforward numerical treatments. The recent implementation of efficient simulation algorithms for high-dimensional systems now…
In phase transition phenomena, the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to. However, this is not an easy task, since a…
We study proper lattice animals for bond- and site-percolation on the hypercubic lattice $\mathbb{Z}^d$ to derive asymptotic series of the percolation threshold $p_c$ in $1/d$, The first few terms of these series were computed in the 1970s,…
A calculation of site-bond percolation thresholds in many lattices in two to five dimensions is presented. The line of threshold values has been parametrized in the literature, but we show here that there are strong deviations from the…
The phenomenon of percolation is one of the core topics in statistical mechanics. It allows one to study the phase transition known in real physical systems only in a purely geometrical way. In this paper, we determine thresholds $p_c$ for…
Extensive Monte-Carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three-dimensional percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered…