Percolation and $O(1)$ loop model

Abstract

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 probabilities. The new approach is more conceptual, less technically demanding, and is amenable to generalizations.

arXiv comment9 pages, 4 figures

References in corpus (5)

• Path Crossing Exponents and the External Perimeter in 2D Percolation
• Critical percolation in the plane
• Multiple-SLE connectivity weights for rectangles, hexagons, and octagons
• Exploration processes and SLE${}_6$
• Critical percolation on mesoscopic triangulations

Cited by in corpus (1)

• Lattice gauge theory and a random-medium Ising model