相关论文: Percolation on two- and three-dimensional lattices
We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation…
We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the best previous…
We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond…
We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, \textbf{87} 052107 (2013)],…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff.
Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random lattices, and…
This paper exhibits a Monte Carlo study on site percolation using the Newmann-Ziff algorithm in distorted square and simple cubic lattices where each site is allowed to be directly linked with any other site if the euclidean separation…
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…
The asymptotic behavior of the percolation threshold $p_c$ and its dependence upon coordination number $z$ is investigated for both site and bond percolation on four-dimensional lattices with compact extended neighborhoods. Simple…
The site percolation problem is one of the core topics in statistical physics. Evaluation of the percolation threshold, which separates two phases (sometimes described as conducting and insulating), is useful for a range of problems from…
We propose two schemes to achieve fast realizations of spatially correlated percolation models. The schemes are shown to be efficient in complementary regimes of correlation phase space. They are combined with a generalized Newman-Ziff…
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…
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…
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…
Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs, significantly increasing the number and variety…
We present a rough estimation -- up to four significant digits, based on the scaling hypothesis and the probability of belonging to the largest cluster vs. the occupation probability -- of the critical occupation probabilities for the…
We propose very efficient algorithms for the bootstrap percolation and the diffusion percolation models by extending the Newman-Ziff algorithm of the classical percolation [M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85 (2000) 4104].…
Rigidity Percolation is a crucial framework for describing rigidity transitions in amorphous systems. We present a new, efficient algorithm to study central-force Rigidity Percolation in two dimensions. This algorithm combines the Pebble…
Site percolation in a distorted simple cubic lattice is characterized numerically employing the Newman-Ziff algorithm. Distortion is administered in the lattice by systematically and randomly dislocating its sites from their regular…