Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance

Abstract

We conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional $Q$-color Potts model. We also provide analogous results for the limit $Q\to 1$ that corresponds to percolation where the observable has a logarithmic singularity. Our conjectures are tested against Monte Carlo simulations showing excellent agreement for $Q=1,2,3$.

29 pages, 9 Figures. Published version: improved discussion, additional numerical tests and references

References in corpus (10)

• 2D growth processes: SLE and Loewner chains
• A conformal bootstrap approach to critical percolation in two dimensions
• The ABC (in any D) of Logarithmic CFT
• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• A solution space for a system of null-state partial differential equations 2
• Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
• Anchored Critical Percolation Clusters and 2-D Electrostatics
• A solution space for a system of null-state partial differential equations 4
• Exact logarithmic four-point functions in the critical two-dimensional Ising model
• Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models

Cited by in corpus (8)

• Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
• On four-point connectivities in the critical 2d Potts model
• Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• Particles, conformal invariance and criticality in pure and disordered systems
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Geometry of bounded critical phenomena
• Numerical Study on a Crossing Probability for the Four-State Potts Model: Logarithmic Correction to the Finite-Size Scaling