Exact logarithmic four-point functions in the critical two-dimensional Ising model

Abstract

Based on conformal symmetry we propose an exact formula for the four-point connectivities of FK clusters in the critical Ising model when the four points are anchored to the boundary. The explicit solution we found displays logarithmic singularities. We check our prediction using Monte Carlo simulations on a triangular lattice, showing excellent agreement. Our findings could shed further light on the formidable task of the characterization of Logarithmic Conformal Field Theories and on their relevance in physics.

5+3 pages, 4 Figures, published version, minor revisions and references added

References in corpus (10)

• 2D growth processes: SLE and Loewner chains
• Associative-algebraic approach to logarithmic conformal field theories
• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• A conformal bootstrap approach to critical percolation in two dimensions
• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• Logarithmic observables in critical percolation
• A solution space for a system of null-state partial differential equations 2
• A formula for crossing probabilities of critical systems inside polygons
• A solution space for a system of null-state partial differential equations 4
• Logarithmic Correlations in Quantum Hall Plateau Transitions

Cited by in corpus (12)

• On four-point connectivities in the critical 2d Potts model
• Open spin chain realization of topological defect on 1d Ising model and boundary and bulk symmetry
• Comments on the Quantum Field Theory of the Coulomb Gas Formalism
• A multicritical Landau-Potts field theory
• Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• Observation of non-scalar and logarithmic correlations in 2D and 3D percolation
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
• Geometry of bounded critical phenomena
• Numerical Study on a Crossing Probability for the Four-State Potts Model: Logarithmic Correction to the Finite-Size Scaling
• Conformal amplitude hierarchy and the Poincare disk