Exact factorization of correlation functions in two-dimensional critical percolation

2007/06/30 by Jacob J H Simmons, Jacob J. H. Simmons, Peter Kleban +1 · 3 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physreve.76.041106

published as Phys.Rev.E76:041106,2007 · 6 pages, 3 figures. Oral presentation given at STATPHYS 23. V2: Minor additions and corrections, figures improved

arxiv created 2007/09/24 · openalex publication_date 2007/10/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By use of conformal field theory, we discover several exact factorizations of higher-order density correlation functions in critical two-dimensional percolation. Our formulas are valid in the upper half-plane, or any conformally equivalent region. We find excellent agreement of our results with high-precision computer simulations. There are indications that our formulas hold more generally.

Citations

• Statistical Mechanics of Fluid Mixtures
• Infinite conformal symmetry in two-dimensional quantum field theory

Cited by

• Percolation in networks with voids and bottlenecks
• Factorization of percolation density correlation functions for clusters touching the sides of a rectangle
• On three-point connectivity in two-dimensional percolation

Related

• Logarithmic correlation functions in 2D critical percolation
• Conformally covariant probabilities, operator product expansions, and logarithmic correlations in two-dimensional critical percolation
• Conformal covariance of connection probabilities and fields in 2D critical percolation
• Conformal Invariance and Percolation
• Conformal Covariance of Connection Probabilities and Fields in 2D Critical Percolation