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Bootstrapping the 3d Ising model at finite temperature

Iliesiu, Luca and Koloğlu, Murat and Simmons-Duffin, David (2019) Bootstrapping the 3d Ising model at finite temperature. Journal of High Energy Physics, 2019 (12). Art. No. 72. ISSN 1126-6708. doi:10.1007/JHEP12(2019)072.

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We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions 〈σσ〉 and 〈ϵϵ〉. As a result, we estimate the one-point functions of the lowest-dimension ℤ₂-even scalar ϵ and the stress energy tensor T_(μν). Our result for 〈σσ〉 at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Iliesiu, Luca0000-0001-7567-7516
Koloğlu, Murat0000-0002-5082-8434
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2019 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: September 30, 2019; Accepted: November 11, 2019; Published: December 9, 2019. We thank Raghu Mahajan and Eric Perlmutter for collaboration in the early stages of this project and many stimulating discussions on finite-temperature physics. We also thank M. Hasenbusch for providing useful references and for sharing unpublished Monte-Carlo results through private correspondence. We additionally thank Tom Hartman and Douglas Stanford for discussions. DSD and MK are supported by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap), a Sloan Research Fellowship, and a DOE Early Career Award under grant No. DE-SC0019085. LVI is supported by Simons Foundation grant 488653.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488657
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0019085
Simons Foundation488653
Subject Keywords:Conformal Field Theory; Field Theories in Lower Dimensions
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Issue or Number:12
Record Number:CaltechAUTHORS:20181119-150919876
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Official Citation:Iliesiu, L., Koloğlu, M. & Simmons-Duffin, D. Bootstrapping the 3d Ising model at finite temperature. J. High Energ. Phys. 2019, 72 (2019) doi:10.1007/JHEP12(2019)072
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91033
Deposited By: Joy Painter
Deposited On:19 Nov 2018 23:14
Last Modified:16 Nov 2021 03:37

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