Percolation in Media with Columnar Disorder

  title={Percolation in Media with Columnar Disorder},
  author={Peter Grassberger and Marcelo R. Hilario and Vladas Sidoravicius},
  journal={Journal of Statistical Physics},
We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have… 

Strict inequality for bond percolation on a dilute lattice with columnar disorder


Let { ξ i } i ≥ 1 be a sequence of i.i.d. positive random variables. Starting from the usual square lattice replace each horizontal edge that links a site in i -th vertical column to another in the (

Percolation of sites not removed by a random walker in d dimensions.

This work systematically explore dependence of the probability Π_{d}(L,u) of percolation (existence of a spanning cluster) of sites not removed by the RW on L and u, which shows the concentration of unvisited sites decays exponentially with increasing u, while the visited sites are highly correlated.

Bernoulli Hyperplane Percolation

We study a dependent site percolation model on the $n$-dimensional Euclidean lattice where, instead of single sites, entire hyperplanes are removed independently at random. We extend the results

PR ] 1 0 Ju l 2 02 0 Bernoulli Hyperplane Percolation

We study a dependent site percolation model on the n-dimensional Euclidean lattice where, instead of single sites, entire hyperplanes are removed independently at random. We extend the results about

A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1



Surface order large deviations for Ising, Potts and percolation models

SummaryWe derive uniform surface order large deviation estimates for the block magnetization in finite volume Ising (or Potts) models with plus or free (or a combination of both) boundary conditions

Three-dimensional percolation with removed lines of sites.

  • Kantor
  • Physics
    Physical review. B, Condensed matter
  • 1986
The site percolation problem on a cubic lattice in which entire lines of sites are removed randomly is analyzed with use of both analytical and large-cell Monte Carlo renormalization-group techniques, and it is shown that the asymptotic values of the critical exponents are consistent with those of regularPercolation.

Critical dynamics of the contact process with quenched disorder.

  • MoreiraDickman
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
The results support the conjecture by Bramson, Durrett, and Schonmann, that in two or more dimensions the disordered CP has only a single phase transition.

Ordinary percolation with discontinuous transitions

This work provides a simple example in the form of a small-world network consisting of a one-dimensional lattice which, when combined with a hierarchy of long-range bonds, reveals many features of this percolation transition in a mathematically rigorous manner.

Agglomerative percolation in two dimensions

We study a process termed agglomerative percolation (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result

Percolation with long-range correlated disorder.

Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as functions of the Hurst exponent H, which

Discontinuous percolation transitions in epidemic processes, surface depinning in random media, and Hamiltonian random graphs.

This work presents and relates the continuous and first-order behaviors in two different classes of models: the first are generalized epidemic processes that describe in their spatially embedded version--either on or off a regular lattice--compact or fractal cluster growth in random media at zero temperature.

Disordered one-dimensional contact process

New theoretical and numerical analysis of the one-dimensional contact process with quenched disorder are presented. We derive new scaling relations, different from their counterparts in the pure

Universality and asymptotic scaling in drilling percolation.

Simulation of a three-dimensional percolation model studied recently by K. Schrenk et al. confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but find indications that the results do not yet represent the true asymptotic behavior.

k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects

The theory of the -core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions is developed and it is demonstrated that a so-called "corona" of the k-core plays a crucial role.