English
Related papers

Related papers: A percolation model with continuously varying expo…

200 papers

We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…

Statistical Mechanics · Physics 2007-05-23 E. Cuansing , H. Nakanishi

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…

Statistical Mechanics · Physics 2016-11-29 M. K. Hassan , M. M. Rahman

Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…

Statistical Mechanics · Physics 2015-07-13 Y. S. Cho , B. Kahng

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…

Statistical Mechanics · Physics 2023-03-08 Grace M. Sommers , Michael J. Gullans , David A. Huse

We study long-range percolation on the hierarchical lattice of order $N$, where any edge of length $k$ is present with probability $p_k=1-\exp(-\beta^{-k} \alpha)$, independently of all other edges. For fixed $\beta$, we show that the…

Probability · Mathematics 2013-05-01 Vyacheslav Koval , Ronald Meester , Pieter Trapman

We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical…

Statistical Mechanics · Physics 2012-12-13 Tom Heitmann , John Gaddy , Wouter Montfrooij

We introduce the Weighted Planar Stochastic Porous Lattice (WPSPL), a geometrically disordered substrate generated by iteratively subdividing a unit square. At each step a block is selected with probability proportional to its area, divided…

Statistical Mechanics · Physics 2026-03-10 Proshanto Kumar , Md. Kamrul Hassan

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…

Statistical Mechanics · Physics 2021-06-14 Yi Hu , Patrick Charbonneau

We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At mean-field level this approach is consistent with the…

Statistical Mechanics · Physics 2014-09-05 Jeferson J. Arenzon , Antonio Coniglio , Annalisa Fierro , Mauro Sellitto

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)],…

Statistical Mechanics · Physics 2014-01-24 Xiao Xu , Junfeng Wang , Jian-Ping Lv , Youjin Deng

We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained…

Statistical Mechanics · Physics 2009-12-10 François Sausset , Cristina Toninelli , Giulio Biroli , Gilles Tarjus

Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken…

Statistical Mechanics · Physics 2012-12-18 Urna Basu , P. K. Mohanty

We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint ${\kappa}_v$ which takes the value $j\in \{0,1,2,3\}$ with probability…

Probability · Mathematics 2021-11-02 Rémy Sanchis , Diogo C. dos Santos , Roger W. C. Silva

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap…

Statistical Mechanics · Physics 2009-11-10 Paolo De Gregorio , Aonghus Lawlor , Phil Bradley , Kenneth A. Dawson

Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [Phys. Rev. Lett. 130, 147101 (2023)], we demonstrated that the correct critical behaviors…

Statistical Mechanics · Physics 2024-09-20 Ming Li , Junfeng Wang , Youjin Deng

Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the…

Statistical Mechanics · Physics 2016-04-12 Deokjae Lee , S. Choi , M. Stippinger , J. Kertész , B. Kahng

We investigate the crossover properties of the frustrated percolation model on a two-dimensional square lattice, with asymmetric distribution of ferromagnetic and antiferromagnetic interactions. We determine the critical exponents nu, gamma…

Statistical Mechanics · Physics 2015-06-25 L. Cannavacciuolo , A. de Candia , A. Coniglio

The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the…

Statistical Mechanics · Physics 2011-10-26 K. J. Schrenk , N. A. M. Araújo , H. J. Herrmann

A new class of lattice gas models with trivial interactions but constrained dynamics are introduced. These are proven to exhibit a dynamical glass transition: above a critical density, rho_c, ergodicity is broken due to the appearance of an…

Statistical Mechanics · Physics 2009-11-11 Cristina Toninelli , Giulio Biroli , Daniel S. Fisher

The compact Abelian Higgs model is simulated on a cubic lattice where it possesses vortex lines and pointlike magnetic monopoles as topological defects. The focus of this high-precision Monte Carlo study is on the vortex network, which is…

High Energy Physics - Lattice · Physics 2008-11-26 Sandro Wenzel , Elmar Bittner , Wolfhard Janke , Adriaan M. J. Schakel