Related papers: Universal scaling functions for bond percolation o…
We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…
We build a multifractal object and use it as a support to study percolation. We identify some differences between percolation in a multifractal and in a regular lattice. We use many samples of finite size lattices and draw the histogram of…
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…
Three-dimensional bond or site percolation theory on a lattice can be interpreted as a gauge theory in which the Wilson loops are viewed as counters of topological linking with random clusters. Beyond the percolation threshold large Wilson…
We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with…
In rotationally constrained percolation models, a site of a percolation cluster could be occupied more than once from different directions due to the nature of the rotational constraint. A state variable $s_i$ is assigned to each lattice…
We present a Monte Carlo study of the bond and site directed (oriented) percolation models in $(d+1)$ dimensions on simple-cubic and body-centered-cubic lattices, with $2 \leq d \leq 7$. A dimensionless ratio is defined, and an analysis of…
The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold Pc=1/2. The calculated probabilities for free boundary…
We report on the exact treatment of a random-matrix representation of bond percolation model on a square lattice in two dimensions with occupation probability $p$. The percolation problem is mapped onto a random complex matrix composed of…
We consider a percolation process in which $k$ points separated by a distance proportional to system size $L$ simultaneously connect together ($k>1$), or a single point at the center of a system connects to the boundary ($k=1$), through…
The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice…
The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functions for the Binder parameter $g$ and the magnetization distribution function $p(m)$ for…
We consider a correlated site percolation problem on a cubic lattice of size $L^3$, with $16\le L\le 512$. The sites of an initially full lattice are removed by a random walk of ${\cal N}=uL^3$ steps. When the parameter $u$ crosses a…
We report on universality in boundary domain growth in cluster aggregation in the limit of maximum concentration. Maximal concentration means that the diffusivity of the clusters is effectively zero and, instead, clusters merge successively…
We study $N$-cluster correlation functions in four- and five-dimensional (4D, 5D) bond percolation by extensive Monte Carlo simulation. We reformulate the transfer Monte Carlo algorithm for percolation [Phys. Rev. E {\bf 72}, 016126 (2005)]…
How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has…
In this paper, site percolation on random $\Phi^{3}$ planar graphs is studied by Monte-Carlo numerical techniques. The method consists in randomly removing a fraction $q=1-p$ of vertices from graphs generated by Monte-Carlo simulations,…
In the bond percolation model on a lattice, we colour vertices with $n_c$ colours independently at random according to Bernoulli distributions. A vertex can receive multiple colours and each of these colours is individually observable. The…
We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to L=512, and estimate the percolation thresholds to be $p_c ({\rm bond})=0.248\,811\,82(10)$ and $p_c ({\rm site})=0.311\,607\,7(2)$. By…
Mixed-wet percolation was introduced recently in the context of two-phase flow in porous media. In this model, the sites of the primal lattice are occupied with a certain probability $p$, and bonds are placed on the dual lattice between two…