Related papers: Crossing Formulae for Critical Percolation in an A…
We prove a formula, first obtained by Kleban, Simmons and Ziff using conformal field theory methods, for the (renormalized) density of a critical percolation cluster in the upper half-plane "anchored" to a point on the real line. The proof…
The logarithmic conformal field theory describing critical percolation is further explored using Watts' determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
Calculations of the production rate of particles with $x>1$ in nuclear collisions due to the interaction of colour strings are presented. Momentum and colour sum rules are used to determine the fragmentation functions of fused strings.…
We argue that clustering of color sources, leading to the percolation transition, may be the way to achieve deconfinement in heavy ion collisions. The critical density for percolation is related to the effective critical temperature of the…
We study the number of clusters in two-dimensional (2d) critical percolation, N_Gamma, which intersect a given subset of bonds, Gamma. In the simplest case, when Gamma is a simple closed curve, N_Gamma is related to the entanglement entropy…
In this work we use the technique of the partial differential approximants to determine, from a pertubative supercritical series expansion for the ulimate survival probability, the critical line of the contact process model in one dimension…
At the critical point in two dimensions, the number of percolation clusters of enclosed area greater than A is proportional to 1/A, with a proportionality constant C that is universal. We show theoretically (based upon Coulomb gas methods),…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
The critical behaviour of several spin models can be simply described as percolation of some suitably defined clusters, or droplets: the onset of the geometrical transition coincides with the critical point and the percolation exponents are…
A scaling theory is used to derive the dependence of the average number <k> of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…
A simple analytical expression, which closely approximates the Coulomb potential between two uniformly charged spheres, is presented. This expression can be used in the optical potential semiclassical analyses which require that the…
In bootstrap percolation it is known that the critical percolation threshold tends to converge slowly to zero with increasing system size, or, inversely, the critical size diverges fast when the percolation probability goes to zero. To…
A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold $p_c\approx 0.655$ is found between…
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…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose…