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# Bootstrapping the 3d Ising model at finite temperature

Iliesiu, Luca and Koloğlu, Murat and Simmons-Duffin, David (2018) Bootstrapping the 3d Ising model at finite temperature. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20181119-150919876

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## Abstract

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 $\langle \sigma\sigma \rangle$ and $\langle \epsilon\epsilon \rangle$. As a result, we estimate the one-point functions of the lowest-dimension $\mathbb Z_2$-even scalar $\epsilon$ and the stress-energy tensor $T_{\mu \nu}$. Our result for $\langle \sigma\sigma \rangle$ at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1811.05451arXivDiscussion Paper
ORCID:
AuthorORCID
Iliesiu, Luca0000-0001-7567-7516
Simmons-Duffin, David0000-0002-2937-9515
Additional Information: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 We also thank M. Hasenbusch for providing useful references and for sharing unpublished Monte-Carlo results through private correspondence.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
Funders:
Funding AgencyGrant Number
Simons Foundation488657
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0019085
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2018-049
Record Number:CaltechAUTHORS:20181119-150919876
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181119-150919876
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91033
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:19 Nov 2018 23:14