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Related papers: Crossover from Isotropic to Directed Percolation

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Based on the field theoretic formulation of the general epidemic process we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine…

Statistical Mechanics · Physics 2009-11-10 Hans-Karl Janssen , Olaf Stenull

Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated…

Disordered Systems and Neural Networks · Physics 2009-11-10 S. Sinha , S. B. Santra

We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, a long-range connection is randomly added to each node $i$ of a square lattice,…

Statistical Mechanics · Physics 2018-09-26 T. B. dos Santos , C. I. N. Sampaio Filho , N. A. M. Araújo , C. L. N. Oliveira , A. A. Moreira

We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic…

Statistical Mechanics · Physics 2009-11-10 Hans-Karl Janssen , Uwe C. Tauber

The directed percolation process in the vicinity of non-equilibrium phase transition is studied by the means of field theoretic methods. It will be assumed that percolation takes place in a compressible environment, which will be generated…

Chaotic Dynamics · Physics 2015-12-21 N. V. Antonov , M. Hnatič , A. S. Kapustin , T. Lučivjanský , L. Mižišin

We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…

Statistical Mechanics · Physics 2009-11-11 S. Lubeck

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically…

Disordered Systems and Neural Networks · Physics 2009-11-11 Santanu Sinha , S. B. Santra

These lectures provide an introduction to the directed percolation and directed animals problems, from a physicist's point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality…

Statistical Mechanics · Physics 2017-03-23 Deepak Dhar

In nature, phase transitions prevail amongst inherently different systems, while frequently showing a universal behavior at their critical point. As a fundamental phenomenon of fluid mechanics, recent studies suggested laminar-turbulent…

Fluid Dynamics · Physics 2018-04-18 Dominik Traphan , Tom T. B. Wester , Gerd Gülker , Joachim Peinke , Pedro G. Lind

It is well established that the phase transition between survival and extinction in spreading models with short-range interactions is generically associated with the directed percolation (DP) universality class. In many realistic spreading…

Statistical Mechanics · Physics 2009-11-13 Hans-Karl Janssen , Olaf Stenull

We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature…

Statistical Mechanics · Physics 2011-04-20 Soumyajyoti Biswas , Anasuya Kundu , Anjan Kumar Chandra

The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…

Disordered Systems and Neural Networks · Physics 2015-05-19 R. A. da Costa , S. N. Dorogovtsev , A. V. Goltsev , J. F. F. Mendes

We examine the interplay between anisotropy and percolation, i.e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model,…

Disordered Systems and Neural Networks · Physics 2017-03-08 Michael A Klatt , Gerd E Schröder-Turk , Klaus Mecke

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

We numerically study the collective dynamics of dense particle assemblies driven by non-reciprocal pairwise forces of amplitude $\kappa$. At a critical value $\kappa_{\rm c}$, the system undergoes a dynamical phase transition from an…

Statistical Mechanics · Physics 2025-10-07 Juliane U. Klamser , Ludovic Berthier

The probability distribution for the number of top to bottom spanning clusters in Directed percolation in two and three dimensions appears to be universal and is of the form $P(n) \sim \exp(-\alpha n^2)$. We argue that $\alpha$ is a new…

Statistical Mechanics · Physics 2007-05-23 Parongama Sen , Somendra M. Bhattacharjee

We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…

Statistical Mechanics · Physics 2015-05-13 Sang-Woo Kim , Jae Dong Noh

We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost…

Probability · Mathematics 2025-10-29 Francesca Cottini , Maximilian Nitzschner

We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…

Statistical Mechanics · Physics 2010-03-19 Yancheng Wang , Wenan Guo , Bernard Nienhuis , Henk W. J. Blöte

This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite…