[Modèle d’Ising en 3D, vu de l’île d’auto-amorçage conforme]
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.
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.
Mot clés : Transitions de phase, Exposants critiques, Symétrie conforme, Modèle d’Ising, Émergence
CC-BY 4.0
@article{CRPHYS_2020__21_2_185_0,
author = {Slava Rychkov},
title = {3D {Ising} model: a view from the conformal bootstrap island},
journal = {Comptes Rendus. Physique},
pages = {185--198},
publisher = {Acad\'emie des sciences, Paris},
volume = {21},
number = {2},
year = {2020},
doi = {10.5802/crphys.23},
language = {en},
}
Slava Rychkov. 3D Ising model: a view from the conformal bootstrap island. Comptes Rendus. Physique, 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/
[1] The conformal bootstrap: theory, numerical techniques, and applications, Rev. Mod. Phys., Volume 91 (2019), 015002 | DOI | MR
[2] EPFL Lectures on Conformal Field Theory in Dimensions, SpringerBriefs in Physics, Springer, 2016
[3] The conformal bootstrap, Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015): Boulder, CO, USA, June 1–26, 2015 (2017), pp. 1-74 | Zbl
[4] Weizmann Lectures on the Numerical Conformal Bootstrap, arXiv: High Energy Physics - Theory (2019), p. 93 (http://arxiv.org/abs/1907.05147)
[5] (“Introduction to Conformal Blocks and Linear Programming. Lectures 1-4”. PhD School “Bootstrap 2020”, https://projects.iq.harvard.edu/bootstrap2020/videos)
[6] Conformal Field Theory, Springer-Verlag, New York, 1997 | DOI | Zbl
[7] Axiomatic conformal theory in dimensions 2 and AdS/CT correspondence, Lett. Math. Phys., Volume 106 (2016) no. 9, pp. 1181-1197 | DOI | MR | Zbl
[8] (“Full vertex algebra and bootstrap – consistency of four point functions in 2d CFT”. 2020, https://arxiv.org/abs/2006.15859)
[9] The Renormalization group and the epsilon expansion, Phys. Rep., Volume 12 (1974), pp. 75-199 | DOI
[10] Nonhamiltonian approach to conformal quantum field theory, Zh. Eksp. Teor. Fiz., Volume 66 (1974), pp. 23-42
[11] Tensor representations of conformal algebra and conformally covariant operator product expansion, Ann. Phys., Volume 76 (1973), pp. 161-188 | DOI | MR
[12] Bounding scalar operator dimensions in 4D CFT, JHEP, Volume 12 (2008), p. 031 | DOI | Zbl
[13] Solving the 3D ising model with the conformal bootstrap, Phys. Rev., Volume D86 (2012), 025022
[14] Solving the 3d ising model with the conformal bootstrap II. c-Minimization and precise critical exponents, J. Stat. Phys., Volume 157 (2014), p. 869 | DOI | MR | Zbl
[15] Bootstrapping mixed correlators in the 3D ising model, JHEP, Volume 11 (2014), p. 109 | DOI
[16] A semidefinite program solver for the conformal bootstrap, JHEP, Volume 06 (2015), p. 174 | DOI
[17] Precision islands in the ising and O(N) models, JHEP, Volume 08 (2016), p. 036 | DOI | Zbl
[18] Finite size scaling study of lattice models in the three-dimensional ising universality class, Phys. Rev. B, Volume 82 (2010), 174433 | DOI
[19] The lightcone bootstrap and the spectrum of the 3d ising CFT, JHEP, Volume 03 (2017), p. 93 | MR | Zbl
[20] Critical phenomena and renormalization-group theory, Phys. Rep., Volume 368 (2002), pp. 549-727 | DOI | MR | Zbl
[21] Critical exponents of the N vector model, J. Phys., Volume A31 (1998), pp. 8103-8121 | MR | Zbl
[22] Critical scattering function in a binary fluid mixture: a study of sodium-deuteroammonia solution at the critical concentration by small-angle neutron scattering, Phys. Rev. B, Volume 40 (1989), pp. 4696-4708 | DOI
[23] Experimental critical-exponent values for fluids, J. Stat. Phys., Volume 137 (2009) no. 5–6, pp. 857-877 | DOI | MR | Zbl
[24] Light scattering and small angle neutron scattering experiments with an aggregating binary liquid mixture of critical composition, Ann. Phys., Volume 506 (1994) no. 1, pp. 1-12 | DOI
[25] Small angle neutron scattering from DO in the critical region, J. Phys.: Condens. Matter, Volume 12 (2000) no. 15, pp. 3531-3542
[26] Universal critical-scattering function: an experimental approach, Phys. Rev. B, Volume 58 (1998), pp. 12038-12043 | DOI
[27] Neutron scattering and the critical behavior of the three-dimensional ising antiferromagnet FEF, Phys. Rev. B, Volume 35 (1987), pp. 4823-4830 | DOI
[28] Statistical Mechanics, Frontiers in Physics, W. A. Benjamin, 1981
[29] Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits, C. R. Math., Volume 333 (2001) no. 3, pp. 239-244 | MR | Zbl
Cité par Sources :
Commentaires - Politique
Dynamics of spatial phase coherence in a dissipative Bose–Hubbard atomic system
Rémy Vatré; Raphaël Bouganne; Manel Bosch Aguilera; ...
C. R. Phys (2023)