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Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents

El-Showk, Sheer and Paulos, Miguel F. and Poland, David and Rychkov, Slava and Simmons-Duffin, David and Vichi, Alessandro (2014) Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents. Journal of Statistical Physics, 157 (4-5). pp. 869-914. ISSN 0022-4715.

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We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z_2 -even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Δ_σ=0.518154(15), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.

Item Type:Article
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URLURL TypeDescription Paper ReadCube access
Poland, David0000-0003-3854-2430
Rychkov, Slava0000-0002-5847-1011
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2014 Springer. Received: 16 April 2014. Accepted: 4 June 2014. Published online: 26 June 2014. We are grateful to M. Hasenbusch, M. Henkel, D. Mouhanna and E. Vicari for the useful communications concerning their work. We are grateful to B. van Rees for the discussions of the interpolating solution. In addition, we thank N. Arkani-Hamed, C. Beem, A. L. Fitzpatrick, G. Fleming, H. Ooguri, H. Osborn, J. Kaplan, E. Katz, F. Kos, J. Maldacena, J. Penedones, L. Rastelli, N. Seiberg, and A. Zhiboedov for related discussions. S. R. is grateful to the Samara Chernorechenskaya Scientific Center for their hospitality. S. R., D. S. D., and D. P. are grateful to KITP for their hospitality. We would also like to thank the organizers and participants of the Back to the Bootstrap 3 conference at CERN. This research was supported in part by the National Science Foundation under Grant No. PHY11-25915. The work of S. E. was partially supported by the French ANR contract 05-BLAN-NT09-573739, the ERC Advanced Grant no. 226371 and the ITN programme PITN-GA-2009-237920. M.P. is supported by DOE Grant DE-FG02-11ER41742. A. V is supported by DOE Grant DE-AC02-05CH1123. The work of D. S. D. is supported by DOE Grant number DE-SC0009988. Computations for this paper were run on National Energy Research Scientific Computing Center supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH1123; on the CERN cluster; on the Aurora and Hyperion clusters supported by the School of Natural Sciences Computing Staff at the Institute for Advanced Study; on the Omega cluster supported by the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center; on the TED cluster of the Chemistry Department and High Energy Theory group at Brown University; and the Kelvin cluster at the C. E. A. Saclay funded by the European Research Council Advanced Investigator Grant ERCAdG228301. S. E. would like to thank D. Kosower for providing access to the Kelvin cluster.
Funding AgencyGrant Number
Agence Nationale pour la Recherche (ANR)05-BLAN-NT09-573739
European Research Council (ERC)226371
Marie Curie FellowshipPITN-GA-2009-237920
Department of Energy (DOE)DE-FG02-11ER41742
Department of Energy (DOE)DE-AC02-05CH1123
Department of Energy (DOE)DE-SC0009988
Department of Energy (DOE)DE-AC02-05CH1123
European Research Council (ERC)228301
Subject Keywords:Critical phenomena Conformal invariance Ising Model Critical exponents Central charge Stress tensor
Issue or Number:4-5
Record Number:CaltechAUTHORS:20170816-100455664
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Official Citation:El-Showk, S., Paulos, M.F., Poland, D. et al. J Stat Phys (2014) 157: 869.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80480
Deposited By: Ruth Sustaita
Deposited On:17 Aug 2017 19:48
Last Modified:20 Nov 2020 20:12

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