Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects.

  title={Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects.},
  author={Johannes Zierenberg and Niklas Fricke and Martin Marenz and Franz Paul Spitzner and Viktoria Blavatska and Wolfhard Janke},
  journal={Physical review. E},
  volume={96 6-1},
We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to… 

Topological effects and conformal invariance in long-range correlated random surfaces

We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a

Level Set Percolation in the Two-Dimensional Gaussian Free Field.

Using a loop-model mapping, it is shown that there is a nontrivial percolation transition and characterize the critical point, and the critical clusters are "logarithmic fractals," whose area scales with the linear size as A∼L^{2}/sqrt[lnL].

Schramm-Loewner evolution and perimeter of percolation clusters of correlated random landscapes

It is shown numerically that in the continuum limit the external perimeter of a percolating cluster of correlated surfaces with H ∈ [−1, 0] is statistically equivalent to SLE curves.

A dynamical model for fractal and compact growth in supercooled systems

A dynamical model that can exhibit both fractal percolation growth and compact circular growth is presented. At any given cluster size, the dimension of a cluster growing on a two-dimensional square

Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions.

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc)

Critical exponent ν of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques

We study the critical behavior of the Ising model in three dimensions on a lattice with site disorder by using Monte Carlo simulations. The disorder is either uncorrelated or long-range correlated

Universality from disorder in the random-bond Blume-Capel model.

Using high-precision Monte Carlo simulations and finite-size scaling the authors study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice and find that it belongs to the universality class of the Ising model with additional logarithmic corrections.

Elongation and percolation of defect motifs in anisotropic packing problems.

The structure of the disclination motifs induced shows that the hexatic-amorphous transition is caused by the growth and connection of disclination grain boundaries, suggesting this transition lies in the percolation universality class in the scenarios considered.

Applications of a neural network to detect the percolating transitions in a system with variable radius of defects.

We systematically study the percolation phase transition at the change of concentration of the chaotic defects (pores) in an extended system where the disordered defects additionally have a variable



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

Long Range Correlated Percolation

In this note we study the field theory of dynamic isotropic percolation (DIP) with quenched randomness that has long range correlations decaying as $r^{-a}$. We argue that the quasi static limit of

Structural and dynamical properties of long-range correlated percolation.

An algorithm for generating long-range correlations in the percolation problem is developed and it is found that the fractal dimensions of the backbone and the red bonds are quite different from uncorrelatedPercolation and vary with \ensuremath{\lambda}, the strength of the correlation.

Scaling laws for random walks in long-range correlated disordered media

We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation

Critical behavior of the random-field Ising magnet with long-range correlated disorder

We study the correlated-disorder driven zero-temperature phase transition of the Random-Field Ising Magnet using exact numerical ground-state calculations for cubic lattices. We consider correlations

Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in

Self-averaging, distribution of pseudocritical temperatures, and finite size scaling in critical disordered systems

The distributions $P(X)$ of singular thermodynamic quantities in an ensemble of quenched random samples of linear size $l$ at the critical point $T_c$ are studied by Monte Carlo in two models. Our

Simultaneous analysis of three-dimensional percolation models

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

Bond and site percolation in three dimensions.

The bond and site percolation models are simulated on a simple-cubic lattice with linear sizes up to L=512, and various universal amplitudes are obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number.

Field-theory approach to critical behavior of systems with long-range correlated defects

A field-theory description of the static and dynamic critical behavior of systems with quenched defects obeying power law correlations ;uxu 2a for large separations x is given. Directly, for