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Result: A conformal bootstrap approach to critical percolation in two dimensions

Title:
A conformal bootstrap approach to critical percolation in two dimensions
Authors:
Picco, Marco, Ribault, Sylvain, Santachiara, Raoul
Source:
SciPost Phys. 1, 009 (2016)
Publication Year:
2016
Collection:
Mathematics
Condensed Matter
High Energy Physics - Theory
Mathematical Physics
Subject Terms:
High Energy Physics - Theory, Condensed Matter - Statistical Mechanics, Mathematical Physics
Document Type:
Report Working Paper
DOI:
10.21468/SciPostPhys.1.1.009
Access URL:
http://arxiv.org/abs/1607.07224
Accession Number:
edsarx.1607.07224
Database:
arXiv

Further Information

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.
Comment: 16 pages, Python code available at https://github.com/ribault/bootstrap-2d-Python, v2: some clarifications and minor improvements