Numerical results for crossing, spanning and wrapping in two-dimensional percolation

TL;DR

This paper uses advanced simulation methods to accurately compute crossing, spanning, and wrapping probabilities in 2D percolation, confirming some predictions and providing new data for theoretical analysis.

Contribution

It introduces highly precise numerical results for 2D percolation probabilities, including new data on wrapping clusters on a cylinder, supporting and extending conformal field theory predictions.

Findings

Results are consistent with conformal field theory predictions.

Provides new data on wrapping clusters on a cylinder.

Achieves high-accuracy numerical calculations for percolation probabilities.

Abstract

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 probabilities in two-dimensional site and bond percolation with exceptional accuracy. Our results are fully consistent with predictions from Conformal Field Theory. We present many new results that await theoretical explanation, particularly for wrapping clusters on a cylinder. We therefore provide possibly the most up-to-date reference for theoreticians working on crossing, spanning and wrapping probabilities in two-dimensional percolation.