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 $$\mathbb{Z}_2$$-even scalar ϵ and the stress energy tensor Tμν. Our result for (σσ) at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.
- Authors:
-
- Princeton Univ., NJ (United States)
- California Inst. of Technology (CalTech), Pasadena, CA (United States)
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1594255
- Grant/Contract Number:
- SC0019085
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 12; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Field Theories in Lower Dimensions
Citation Formats
Iliesiu, Luca, Koloğlu, Murat, and Simmons-Duffin, David. Bootstrapping the 3d Ising model at finite temperature. United States: N. p., 2019.
Web. doi:10.1007/JHEP12(2019)072.
Iliesiu, Luca, Koloğlu, Murat, & Simmons-Duffin, David. Bootstrapping the 3d Ising model at finite temperature. United States. https://doi.org/10.1007/JHEP12(2019)072
Iliesiu, Luca, Koloğlu, Murat, and Simmons-Duffin, David. Mon .
"Bootstrapping the 3d Ising model at finite temperature". United States. https://doi.org/10.1007/JHEP12(2019)072. https://www.osti.gov/servlets/purl/1594255.
@article{osti_1594255,
title = {Bootstrapping the 3d Ising model at finite temperature},
author = {Iliesiu, Luca and Koloğlu, Murat and Simmons-Duffin, David},
abstractNote = {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 $\mathbb{Z}_2$-even scalar ϵ and the stress energy tensor Tμν. Our result for (σσ) at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.},
doi = {10.1007/JHEP12(2019)072},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2019,
place = {United States},
year = {Mon Dec 09 00:00:00 EST 2019},
month = {Mon Dec 09 00:00:00 EST 2019}
}
Works referenced in this record:
Universality at large transverse spin in defect CFT
journal, September 2018
- Lemos, Madalena; Liendo, Pedro; Meineri, Marco
- Journal of High Energy Physics, Vol. 2018, Issue 9
Carving out the space of 4D CFTs
journal, May 2012
- Poland, David; Simmons-Duffin, David; Vichi, Alessandro
- Journal of High Energy Physics, Vol. 2012, Issue 5
Finite size scaling study of lattice models in the three-dimensional Ising universality class
journal, November 2010
- Hasenbusch, Martin
- Physical Review B, Vol. 82, Issue 17
Large Spin Perturbation Theory for Conformal Field Theories
journal, September 2017
- Alday, Luis F.
- Physical Review Letters, Vol. 119, Issue 11
Casimir forces in binary liquid mixtures
journal, August 1997
- Krech, Michael
- Physical Review E, Vol. 56, Issue 2
The analytic bootstrap and AdS superhorizon locality
journal, December 2013
- Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David
- Journal of High Energy Physics, Vol. 2013, Issue 12
Precision islands in the Ising and O(N ) models
journal, August 2016
- Kos, Filip; Poland, David; Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2016, Issue 8
Bounds on 4D conformal and superconformal field theories
journal, May 2011
- Poland, David; Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2011, Issue 5
A universal inequality for CFT and quantum gravity
journal, August 2011
- Hellerman, Simeon
- Journal of High Energy Physics, Vol. 2011, Issue 8
Positivity constraints for anomalous dimensions
journal, October 1973
- Nachtmann, Otto
- Nuclear Physics B, Vol. 63
An algebraic approach to the analytic bootstrap
journal, April 2017
- Alday, Luis F.; Zhiboedov, Alexander
- Journal of High Energy Physics, Vol. 2017, Issue 4
Bounds for OPE coefficients on the Regge trajectory
journal, October 2017
- Costa, Miguel S.; Hansen, Tobias; Penedones, João
- Journal of High Energy Physics, Vol. 2017, Issue 10
Constraints on Conformal Field Theories in Diverse Dimensions from the Bootstrap Mechanism
journal, October 2013
- Gliozzi, Ferdinando
- Physical Review Letters, Vol. 111, Issue 16
Convexity and liberation at large spin
journal, November 2013
- Komargodski, Zohar; Zhiboedov, Alexander
- Journal of High Energy Physics, Vol. 2013, Issue 11
The conformal bootstrap at finite temperature
journal, October 2018
- Iliesiu, Luca; Koloğlu, Murat; Mahajan, Raghu
- Journal of High Energy Physics, Vol. 2018, Issue 10
Boundary and interface CFTs from the conformal bootstrap
journal, May 2015
- Gliozzi, Ferdinando; Liendo, Pedro; Meineri, Marco
- Journal of High Energy Physics, Vol. 2015, Issue 5
Analyticity in spin in conformal theories
journal, September 2017
- Caron-Huot, Simon
- Journal of High Energy Physics, Vol. 2017, Issue 9
Bounding scalar operator dimensions in 4 D CFT
journal, December 2008
- Rattazzi, Riccardo; Rychkov, Vyacheslav S.; Tonni, Erik
- Journal of High Energy Physics, Vol. 2008, Issue 12
The bootstrap program for boundary CFT d
journal, July 2013
- Liendo, Pedro; Rastelli, Leonardo; van Rees, Balt C.
- Journal of High Energy Physics, Vol. 2013, Issue 7
Radial coordinates for defect CFTs
journal, November 2018
- Lauria, Edoardo; Meineri, Marco; Trevisani, Emilio
- Journal of High Energy Physics, Vol. 2018, Issue 11
Bootstrapping Conformal Field Theories with the Extremal Functional Method
journal, December 2013
- El-Showk, Sheer; Paulos, Miguel F.
- Physical Review Letters, Vol. 111, Issue 24
Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
journal, October 1999
- Campostrini, Massimo; Pelissetto, Andrea; Rossi, Paolo
- Physical Review E, Vol. 60, Issue 4
Emergent spacetime and holographic CFTs
journal, October 2012
- El-Showk, Sheer; Papadodimas, Kyriakos
- Journal of High Energy Physics, Vol. 2012, Issue 10
Light-ray operators in conformal field theory
journal, November 2018
- Kravchuk, Petr; Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2018, Issue 11
Conformal bootstrap with slightly broken higher spin symmetry
journal, June 2016
- Alday, Luis F.; Zhiboedov, Alexander
- Journal of High Energy Physics, Vol. 2016, Issue 6
The lightcone bootstrap and the spectrum of the 3d Ising CFT
journal, March 2017
- Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2017, Issue 3
The Mellin formalism for boundary CFT d
journal, October 2017
- Rastelli, Leonardo; Zhou, Xinan
- Journal of High Energy Physics, Vol. 2017, Issue 10
A semidefinite program solver for the conformal bootstrap
journal, June 2015
- Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2015, Issue 6
Critical exponents of the 3d Ising and related models from conformal bootstrap
journal, October 2014
- Gliozzi, Ferdinando; Rago, Antonio
- Journal of High Energy Physics, Vol. 2014, Issue 10
Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014
- Kos, Filip; Poland, David; Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2014, Issue 11
A spacetime derivation of the Lorentzian OPE inversion formula
journal, July 2018
- Simmons-Duffin, David; Stanford, Douglas; Witten, Edward
- Journal of High Energy Physics, Vol. 2018, Issue 7
Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects
journal, January 2017
- Liendo, Pedro; Meneghelli, Carlo
- Journal of High Energy Physics, Vol. 2017, Issue 1
Solving the 3D Ising model with the conformal bootstrap
journal, July 2012
- El-Showk, Sheer; Paulos, Miguel F.; Poland, David
- Physical Review D, Vol. 86, Issue 2
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents
journal, June 2014
- El-Showk, Sheer; Paulos, Miguel F.; Poland, David
- Journal of Statistical Physics, Vol. 157, Issue 4-5
The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019
- Poland, David; Rychkov, Slava; Vichi, Alessandro
- Reviews of Modern Physics, Vol. 91, Issue 1
Defects in conformal field theory
journal, April 2016
- Billò, Marco; Gonçalves, Vasco; Lauria, Edoardo
- Journal of High Energy Physics, Vol. 2016, Issue 4
Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
journal, April 2009
- Vasilyev, O.; Gambassi, A.; Maciołek, A.
- Physical Review E, Vol. 79, Issue 4