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

TL;DR

This paper uses integrable field theory to predict universal crossing probabilities and the expected number of crossing clusters in near-critical two-dimensional percolation, providing insights into critical phenomena.

Contribution

It introduces a novel application of integrable field theory to derive universal predictions for crossing probabilities and cluster counts near criticality in 2D percolation.

Findings

Universal crossing probability predictions near criticality

Mean number of crossing clusters derived

Application of integrable field theory to 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.