Exact Logarithmic Four-Point Functions in the Critical Two-Dimensional Ising Model

Year: 2017

Authors: Gori G., Viti J.

Autors Affiliation: SISSA, Via Bonomea 265, I-34136 Trieste, Italy; CNR IOM, Via Bonomea 265, I-34136 Trieste, Italy; Univ Fed Rio Grande do Norte, ECT, BR-59078970 Natal, RN, Brazil; Univ Fed Rio Grande do Norte, Inst Int Fis, BR-59078970 Natal, RN, Brazil.

Abstract: Based on conformal symmetry we propose an exact formula for the four-point connectivities of Fortuin-Kasteleyn 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.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 119 (19)      Pages from: 191601-1  to: 191601-6

KeyWords: Solution Space; Field-theory; Critical Percolation; System; Operators; Symmetry; Algebras; Sle
DOI: 10.1103/PhysRevLett.119.191601