English
Related papers

Related papers: Percolation in a simple cubic lattice with distort…

200 papers

In this paper we introduce a variant of the honeycomb lattice in which we create defects by randomly exchanging adjacent bonds, producing a random tiling with a distribution of polygon edges. We study the percolation properties on these…

Disordered Systems and Neural Networks · Physics 2016-05-04 Meryl A. Spencer , Robert M. Ziff

Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven…

Statistical Mechanics · Physics 2009-11-10 Dirk Osterkamp , Dietrich Stauffer , Amnon Aharony

A model named `Colored Percolation' has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability $p$ and are then colored by one of the $n$ distinct colors…

Statistical Mechanics · Physics 2017-09-13 Sumanta Kundu , S. S. Manna

We present a method for computing transition points of the random cluster model using a generalization of the Newman-Ziff algorithm, a celebrated technique in numerical percolation, to the random cluster model. The new method is…

A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows…

Statistical Mechanics · Physics 2009-10-31 Iwan Jensen

We prove a remarkable combinatorial symmetry in the number of spanning configurations in site percolation: for a large class of lattices, the number of spanning configurations with an odd or even number of occupied sites differs by $\pm 1$.…

Statistical Mechanics · Physics 2019-12-11 Stephan Mertens , Cristopher Moore

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…

Statistical Mechanics · Physics 2025-11-04 W. S. Oliveira , J. Pimentel de Lima , Raimundo R. dos Santos

Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…

Statistical Mechanics · Physics 2022-02-22 Abraham Levitan

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…

Soft Condensed Matter · Physics 2026-02-12 Nina Javerzat , Daniele Notarmuzi

We study site percolation on a square lattice with random compact diamond-shaped neighborhoods. Each site $s$ is connected to others within a neighborhood in the shape of a diamond of radius $r_s$, where $r_s$ is uniformly chosen from the…

Statistical Mechanics · Physics 2026-02-05 Charles S. do Amaral , Mateus G. Soares , Robert M. Ziff

The social percolation model \citep{solomon-et-00} considers a 2-dimensional regular lattice. Each site is occupied by an agent with a preference $x_{i}$ sampled from a uniform distribution $U[0,1]$. Agents transfer the information about…

Physics and Society · Physics 2021-03-17 Frank Schweitzer

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…

Disordered Systems and Neural Networks · Physics 2020-07-08 S. S. Manna , Robert M. Ziff

The Peierls distortions in a two-dimensional electron-lattice system described by a Su-Schrieffer-Heeger type model extended to two-dimensions are numerically studied for a square lattice. The electronic band is just half-filled and the…

Materials Science · Physics 2015-06-24 Yoshiyuki Ono , Tetsuya Hamano

We present a percolation model that is inspired by recent works on immiscible two-phase flow in a mixed-wet porous medium made of a mixture of grains with two different wettability properties. The percolation model is constructed on a dual…

Statistical Mechanics · Physics 2025-09-24 Jnana Ranjan Das , Santanu Sinha , Alex Hansen , Sitangshu B. Santra

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…

Statistical Mechanics · Physics 2009-10-31 M. E. J. Newman , R. M. Ziff

We show analytically that the $[0,1]$, $[1,1]$ and $[2,1]$ Pad{\'e} approximants of the mean cluster number $S(p)$ for site and bond percolation on general $d$-dimensional lattices are upper bounds on this quantity in any Euclidean…

Statistical Mechanics · Physics 2015-06-12 Salvatore Torquato , Yang Jiao

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…

Condensed Matter · Physics 2009-10-22 Y. Leroyer , E. Pommiers

We study the effect of positive correlations on the critical threshold of site and bond percolation in a square lattice with d = 2. We propose two algorithms for generating dependent lattices with minimal correlation length and non-negative…

Statistical Mechanics · Physics 2014-02-13 Navid Dianati , YenTing Lin

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…

Disordered Systems and Neural Networks · Physics 2015-06-25 Yuriy Yu. Tarasevich , Steven C. van der Marck

Percolation on a five-dimensional simple hypercubic (sc(5)) lattice with extended neighborhoods is investigated by means of extensive Monte Carlo simulations, using an effective single-cluster growth algorithm. The critical exponents,…

Statistical Mechanics · Physics 2025-12-29 Zhipeng Xun , Dapeng Hao , Robert M. Ziff