Bootstrapping the 3d Ising model at finite temperature
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 〈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.
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 We also thank M. Hasenbusch for providing useful references and for sharing unpublished Monte-Carlo results through private correspondence.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.Attached Files
Published - Iliesiu2019_Article_BootstrappingThe3dIsingModelAt.pdf
Submitted - 1811.05451.pdf
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Additional details
- Eprint ID
- 91033
- Resolver ID
- CaltechAUTHORS:20181119-150919876
- 488657
- Simons Foundation
- Alfred P. Sloan Foundation
- DE-SC0019085
- Department of Energy (DOE)
- 488653
- Simons Foundation
- SCOAP3
- Created
-
2018-11-19Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2018-049