3D Ising model: a view from the conformal bootstrap island

Slava Rychkov

doi:10.5802/crphys.23

3D Ising model: a view from the conformal bootstrap island

Slava Rychkov ^1,²

¹ Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
² Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France

Comptes Rendus. Physique, Prizes of the French Academy of Sciences 2019, Volume 21 (2020) no. 2, pp. 185-198.

Abstract
Résumé

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space.

Nous expliquerons comment utiliser les axiomes de la théorie conforme des champs pour faire des prédictions sur les exposants critiques des transitions de phase continues en trois dimensions, par une procédure dite “auto-amorçage conforme”. La méthode consiste à faire l’hypothèse que les fonctions de corrélation ont l’invariance conforme, puis à imposer certaines relations entre les fonctions de corrélation d’ordre différent. L’analyse numérique montre alors que ces conditions ne sont compatibles que si les exposants critiques ont des valeurs particulières, plus précisément s’ils se trouvent dans un îlot étroit de l’espace des paramètres.

Published online: 2020-11-03

DOI: 10.5802/crphys.23

Keywords: Phase transitions, Critical exponents, Conformal symmetry, Ising model, Emergence
Mots-clés : Transitions de phase, Exposants critiques, Symétrie conforme, Modèle d’Ising, Émergence

Author's affiliations:

Slava Rychkov ^{1, 2}

¹ Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
² Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {3D {Ising} model: a view from the conformal bootstrap island},
     journal = {Comptes Rendus. Physique},
     pages = {185--198},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2020},
     doi = {10.5802/crphys.23},
     language = {en},
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Slava Rychkov. 3D Ising model: a view from the conformal bootstrap island. Comptes Rendus. Physique, Prizes of the French Academy of Sciences 2019, Volume 21 (2020) no. 2, pp. 185-198. doi : 10.5802/crphys.23. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.23/

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