Crossing probability and number of crossing clusters in off-critical percolation

Abstract

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 sides much larger than the correlation length and for the mean number of such crossing clusters.

13 pages, 5 figures. Published version with references, appendix and comparison with numerics added

References in corpus (4)

• Potts q-color field theory and scaling random cluster model
• Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT
• Universal amplitude ratios of two-dimensional percolation from field theory
• Mapping functions and critical behavior of percolation on rectangular domains

Cited by in corpus (8)

• Phase separation and interface structure in two dimensions from field theory
• Classifying Potts critical lines
• Fields, particles and universality in two dimensions
• On superuniversality in the $q$-state Potts model with quenched disorder
• Particles, conformal invariance and criticality in pure and disordered systems
• Critical points in coupled Potts models and correlated percolation
• Percolation crossing probabilities in hexagons: a numerical study
• Continuum Percolation on Disoriented Surfaces: the Problem of Permeable Disks on a Klein Bottle