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.

9 pages, 4 figures

References in corpus (1)

• Critical percolation in the plane

Cited by in corpus (1)

• Lattice gauge theory and a random-medium Ising model