English
Related papers

Related papers: Universality classes for percolation models with l…

200 papers

Bootstrap percolation is a wide class of monotone cellular automata with random initial state. In this work we develop tools for studying in full generality one of the three `universality' classes of bootstrap percolation models in two…

Probability · Mathematics 2021-12-07 Ivailo Hartarsky

With respect to a class of long-range exclusion processes on $\mathbb{Z}^d$, with single particle transition rates of order $|\cdot|^{-(d+\alpha)}$, starting under Bernoulli invariant measure $\nu_\rho$ with density $\rho$, we consider the…

Probability · Mathematics 2014-07-31 Cédric Bernardin , Patrícia Gonçalves , Sunder Sethuraman

Locality imposes stringent constraints on the spreading of information in nonrelativistic quantum systems, which is reminiscent of a "light-cone," a casual structure arising in their relativistic counterparts. Long-range interactions can…

Disordered Systems and Neural Networks · Physics 2019-02-06 David J. Luitz , Yevgeny Bar Lev

A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…

Chaotic Dynamics · Physics 2012-03-28 Giorgio Krstulovic , Rehab Bitane , Jeremie Bec

We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…

Statistical Mechanics · Physics 2015-06-25 Luca Delfini , Stefano Lepri , Roberto Livi , Antonio Politi

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

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The…

Statistical Mechanics · Physics 2017-03-16 Alexis Poncet , Olivier Bénichou , Vincent Démery , Gleb Oshanin

We present some exact results on the behavior of Branching and Annihilating Random Walks, both in the Directed Percolation and Parity Conserving universality classes. Contrary to usual perturbation theory, we perform an expansion in the…

Statistical Mechanics · Physics 2013-05-29 Federico Benitez , Nicolas Wschebor

Following the approach outlined in [18], convergence to SLE6 of the Exploration Processes for the correlated bond-triangular type models studied in [7] is established. This puts the said models in the same universality class as the standard…

Mathematical Physics · Physics 2010-04-27 I. Binder , L. Chayes , H. K. Lei

We consider face and cycle percolation as models for continuum percolation based on random simplicial complexes in Euclidean space. Face percolation is defined through infinite sequences of $d$-simplices sharing a $(d-1)$-dimensional face.…

Probability · Mathematics 2022-12-14 Christian Hirsch , Daniel Valesin

Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…

Statistical Mechanics · Physics 2023-07-27 Carl Fredrik Berg , Muhammad Sahimi

In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of…

Strongly Correlated Electrons · Physics 2015-03-17 R. Jafari

The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are…

Statistical Mechanics · Physics 2021-05-12 Salvatore Torquato , Jaeuk Kim , Michael A. Klatt

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical…

Statistical Mechanics · Physics 2009-10-31 Bosiljka Tadic

Here we compare critical properties of systems in the directed-percolation (DP) universality class with those of absorbing-state phase transitions occurring in the presence of a non-diffusive conserved field, i.e. transitions in the…

Statistical Mechanics · Physics 2009-11-13 Juan A. Bonachela , Miguel A. Munoz

We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…

Probability · Mathematics 2022-09-30 Ercan Sönmez , Arnaud Rousselle

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…

Statistical Mechanics · Physics 2009-11-07 Santo Fortunato

We analyse scaling laws that govern macromolecules of different topology: polymer chains, homogeneous and miktoarm star polymers in a good solvent possibly constrained by a porous medium. The latter is modelled by long-range-correlated…

Soft Condensed Matter · Physics 2015-05-13 V. Blavatska , C. von Ferber , Yu. Holovatch

A model of directed percolation processes with colors and flavors that is equivalent to a population model with many species near their extinction thresholds is presented. We use renormalized field theory and demonstrate that all…

Statistical Mechanics · Physics 2007-05-23 Hans-Karl Janssen

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…

Statistical Mechanics · Physics 2012-12-11 Stephan Mertens , Cristopher Moore