A conformal bootstrap approach to critical percolation in two dimensions

TL;DR

This paper applies a conformal bootstrap method to analyze critical percolation in two dimensions, proposing an exact spectrum ansatz and validating results with Monte Carlo simulations.

Contribution

It introduces a novel spectrum ansatz for 2D critical percolation and uses numerical bootstrap to compute four-point functions, matching Monte Carlo results.

Findings

Spectrum ansatz matches Monte Carlo data

Four-point functions computed numerically

Results confirm theoretical predictions

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.