A conformal bootstrap approach to critical percolation in two dimensions
arXiv:1607.07224 · doi:10.21468/SciPostPhys.1.1.009
Abstract
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.
16 pages, Python code available at https://github.com/ribault/bootstrap-2d-Python, v2: some clarifications and minor improvements