A conformal bootstrap approach to critical percolation in two dimensions

Marco Picco 1 Sylvain Ribault 2 Raoul Santachiara 3

SciPost Physics, 2016, <10.21468/SciPostPhys.1.1.009>

We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.

  • 1. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
  • 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681
  • 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques