Related papers: Crossover from Isotropic to Directed Percolation
Collective tunneling is a ubiquitous phenomenon in finite-size spin clusters that shows up in systems as diverse as molecular magnets or spin clusters adsorbed at surfaces. The problem we explore is to understand how small flipping terms…
Percolation in an information-theoretically secure graph is considered where both the legitimate and the eavesdropper nodes are distributed as Poisson point processes. For both the path-loss and the path-loss plus fading model, upper and…
We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet…
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…
The dynamical properties of the invasion percolation on the square lattice are investigated with emphasis on the geometrical properties on the growing cluster of infected sites. The exterior frontier of this cluster forms a critical loop…
We consider bond percolation on $\Z^d\times \Z^s$ where edges of $\Z^d$ are open with probability $p<p_c(\Z^d)$ and edges of $\Z^s$ are open with probability $q$, independently of all others. We obtain bounds for the critical curve in $(p,…
The Fortuin-Kasteleyn mapping between the Ising model and the site-bond correlated percolation model is shown to be only one of an infinite class of exact mappings. These new cluster representations are a result of "renormalized"…
The paramagnetic-ferromagnetic transition in the Ising model can be described as percolation of suitably defined clusters. We have tried to extend such picture to the confinement-deconfinement transition of SU(2) pure gauge theory, which is…
We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height functions of the limit are described as certain diffusive…
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…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
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…
When conducting bonds are occupied randomly in a two-dimensional square lattice, the conductivity of the system increases continuously as the density of those conducting bonds exceeds the percolation threshold. Such a behavior is well known…
Many real-world infrastructures, from sensor and road networks to power grids, are spatially embedded and anisotropic, with constraints on the maximum number of links each node can establish. Such systems can be represented as anisotropic…
An exact formula is given for the probability that there exists a spanning cluster between opposite boundaries of an annulus, in the scaling limit of critical percolation. The entire distribution function for the number of distinct spanning…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
We introduce and investigate a simple model to describe recent experiments by Douady and Daerr on flowing sand. The model reproduces experimentally observed compact avalanches, whose opening angle decreases linearly as a threshold is…
We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field…
We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the…
Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of…