Description
I'll briefly review how conformal techniques can be applied to calculate geometrical observables in 2d critical statistical models. Typical examples include crossing probabilities and connectivies in percolation and the Q-state Potts model. I'll then show a concrete example for the Ising model, in which a four point connectivity can be exactly determined and compared against Monte-Carlo simulations. The example is particularly relavant because it provides a rare instance of a logarithmic singularity in a conformal invariant quantum field theory.
Joint work with G. Gori (SISSA), arXiv:1704.02893, Phys. Rev. Lett. 119, 191601 (2017)