Percolation and O(1) loop model

2021/11/30 by Mikhail Khristoforov, Stanislav Smirnov, Khristoforov, Mikhail +1 · 1 citation
Mathematics · Physics and Astronomy · #30C35 #60K35 (Primary) #81T40 #82B43 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2111.15612

openalex publication_date 2021/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an "ultimate" proof of Cardy's formula for the critical percolation on the hexagonal lattice \citeSmirnov01criticalpercolation, 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.

Citations

• The energy density in the planar Ising model

Cited by

• Planar percolation and the loop O(n) model

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