Non-gaussianity of the critical 3d Ising model

Creators: Rychkov, Slava; Simmons-Duffin, David; Zan, Bernardo

Abstract

We discuss the 4pt function of the critical 3d Ising model, extracted from recent conformal bootstrap results. We focus on the non-gaussianity Q - the ratio of the 4pt function to its gaussian part given by three Wick contractions. This ratio reveals significant non-gaussianity of the critical fluctuations. The bootstrap results are consistent with a rigorous inequality due to Lebowitz and Aizenman, which limits Q to lie between 1/3 and 1.

Additional Information

© 2017 Rychkov et al. This work is licensed under the Creative Commons. Received 22-12-2016 Accepted 08-02-2017 Published 10-02-2017 SR is grateful to IHES where this work was initiated, and especially to Hugo Duminil-Copin for explaining the Lebowitz-Aizenman inequality. DSD thanks Clay Córdova for discussions. We thank Ulli Wolff for pointing out [15, 16]. SR and BZ are supported by the National Centre of Competence in Research SwissMAP funded by the Swiss National Science Foundation. DSD is supported by DOE grant number DE-SC0009988 and a William D. Loughlin Membership at the Institute for Advanced Study. DSD and SR are supported by the Simons Foundation grants 488655 and 488657 (Simons collaboration on the Non-perturbative bootstrap).

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