Related papers: Comment on: "Superscaling of Percolation on Rectan…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…
We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of…
We investigate finite size scaling in percolating widthless stick systems with variable aspect ratios in an extensive Monte Carlo simulation study. A generalized scaling function is introduced to describe the scaling behavior of the…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
Scale-invariant universal crossing probabilities are studied for critical anisotropic systems in two dimensions. For weakly anisotropic standard percolation in a rectangular-shaped system, Cardy's exact formula is generalized using a…
This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…
We show that spatial variation and correlation of superconductivity fluctuations in a two-band model are scaled by two characteristic lengths. This results in substantially more complicated picture compared to one-band systems. In…
Survival and percolation probabilities are most important quantities in the theory and in the application of growth models with spreading. We construct field theoretical expressions for these probabilities which are feasible for…
Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of…
We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical…
The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range…
A supersymmetric theory with several scalar superfields generically has several domain wall type classical configurations which interpolate between various supersymmetric vacua of the scalar fields. Depending on the couplings, some of these…
In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function…
Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability…
Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.
Spiral (gyrotropic) percolation which is related to the behavior of an electron system in strong magnetic fields is studied. It is shown that the scaling behavior area near the percolation threshold is anomalously narrow. The percolation…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
We consider a special class of quasi-periodic potentials arising in the physics of photonic systems and possessing rotational symmetry of the 8th order. We are interested in the ``scaling'' properties of such potentials, namely, the growth…