A conformal bootstrap approach to critical percolation in two dimensions

2016/07/31 by Marco Picco, Sylvain Ribault, Raoul Santachiara · 2 citations
Physics and Astronomy · Mathematics · #hep-th #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.21468/scipostphys.1.1.009

published as SciPost Phys. 1, 009 (2016) · 16 pages, Python code available at https://github.com/ribault/bootstrap-2d-Python, v2: some clarifications and minor improvements

arxiv created 2016/10/17 · arxiv updated 2018/04/20

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.

Cited by

• Bootstrap approach to geometrical four-point functions in the two-dimensional critical Q-state Potts model: A study of the s-channel spectra
• Four-point geometrical correlation functions in the two-dimensional Q-state Potts model: connections with the RSOS models

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