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

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 -> 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. © 2018, The Author(s).