On three-point connectivity in two-dimensional percolation

Abstract

We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.

10 pages, 1 figure

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Cited by in corpus (54)

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• Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model
• Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
• Conformal bootstrap for percolation and polymers
• Classifying Potts critical lines
• The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0
• Short-range correlations in percolation at criticality
• Local logarithmic correlators as limits of Coulomb gas integrals
• The action of the Virasoro algebra in the two-dimensional Potts and loop models at generic $Q$
• Factorization of correlations in two-dimensional percolation on the plane and torus
• Exact logarithmic four-point functions in the critical two-dimensional Ising model
• Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models
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• Four-point geometrical correlation functions in the two-dimensional $Q$-state Potts model: connections with the RSOS models
• Comments on the Quantum Field Theory of the Coulomb Gas Formalism
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• Integrability of Conformal Loop Ensemble: Imaginary DOZZ Formula and Beyond
• Conformally invariant boundary conditions in the antiferromagnetic Potts model and the $SL(2,\mathbb{R})/U(1)$ sigma model
• The fully packed loop model as a non-rational $W_3$ conformal field theory
• Particles, conformal invariance and criticality in pure and disordered systems
• Bond percolation between $k$ separated points on a square lattice
• Spin clusters and conformal field theory
• Four spins correlation function of the $q$ states Potts model, for general values of $q$. Its percolation model limit $q\to 1$
• Evidences of conformal invariance in 2d rigidity percolation
• Schramm-Loewner evolution in 2d rigidity percolation
• Critical loop models are exactly solvable
• The two upper critical dimensions of the Ising and Potts models
• Correlation function of four spins in the percolation model
• Analytic continuation of 3-point functions of the conformal field theory
• Global symmetry and conformal bootstrap in the two-dimensional $Q$-state Potts model
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• On the CFT describing the spin clusters in 2d Potts model
• Critical points in coupled Potts models and correlated percolation
• Critical points in the $C{P}^{N-1}$ model
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
• Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics
• Nonuniversality in random criticality
• The imaginary Toda field theory
• Three-point functions in the fully packed loop model on the honeycomb lattice
• Universal correlations in percolation
• Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model
• Rate of cluster decomposition via Fermat-Steiner point
• On the analytical continuation of lattice Liouville theory
• Logarithmic operators in $c=0$ bulk CFTs
• Backbone three-point correlation function in the two-dimensional Potts model
• Factorization Formulas for $2D$ Critical Percolation, Revisited