Related papers: A crossing probability for critical percolation in…
Using conformal field theory, we derive several new crossing formulas at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy's formula for the…
In this article, we generalize known formulas for crossing probabilities. Prior crossing results date back to J. Cardy's prediction of a formula for the probability that a percolation cluster in two dimensions connects the left and right…
Probabilities of crossing on same-spin clusters, seen as order parameters, have been introduced recently for the critical 2d Ising model by Langlands, Lewis and Saint-Aubin. We extend Cardy's ideas, introduced for percolation, to obtain an…
We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we will consider the convergence of critical crossing probabilities to Cardy's formula and of the critical exploration path to…
Several formulas for crossing functions arising in the continuum limit of critical two-dimensional percolation models are studied. These include Watts's formula for the horizontal-vertical crossing probability and Cardy's new formula for…
Crossing probabilities for critical 2-D percolation on large but finite lattices have been derived via boundary conformal field theory. These predictions agree very well with numerical results. However, their derivation is heuristic and…
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 present study of finite-size scaling and universality of crossing probabilities for the $q$-state Potts model. Crossing probabilities of the Potts model are similar ones in percolation problem. We numerically investigated scaling of…
The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for…
We examine crossing probabilities and free energies for conformally invariant critical 2-D systems in rectangular geometries, derived via conformal field theory and Stochastic L\"owner Evolution methods. These quantities are shown to…
The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails…
We present an "ultimate" proof of Cardy's formula for the critical percolation on the hexagonal lattice \cite{Smirnov01criticalpercolation}, showing the existence of the universal and conformally invariant scaling limit of crossing…
The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold Pc=1/2. The calculated probabilities for free boundary…
Making use of a recent complete calculation of a chiral six-point correlation function C(z) in a rectangle we calculate various quantities of interest for percolation (SLE parameter \kappa = 6) and many other two-dimensional critical…
We show the existence of a scaling limit for the crossing probabilities on the square lattice in an equilateral triangle for the critical percolation. We also show that Cardy's formula does not hold on the square lattice for the critical…
G. M. T. Watts derived that in two dimensional critical percolation the crossing probability Pi_hv satisfies a fifth order differential equation which includes another one of third order whose independent solutions describe the physically…
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…
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…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a…