A conformal bootstrap approach to critical percolation in two dimensions
High Energy Physics - Theory
2018-04-20 v2 Statistical Mechanics
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1607.07224,
title = {A conformal bootstrap approach to critical percolation in two dimensions},
author = {Marco Picco and Sylvain Ribault and Raoul Santachiara},
journal= {arXiv preprint arXiv:1607.07224},
year = {2018}
}
Comments
16 pages, Python code available at https://github.com/ribault/bootstrap-2d-Python, v2: some clarifications and minor improvements