Preprint

PUBDB-2023-06458

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Analytic and numerical bootstrap for the long-range Ising model

Behan, C. ; Lauria, E. (Corresponding author) ; Nocchi, M. ; van Vliet, P.Extern*

2023

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Please use a persistent id in citations: doi:10.3204/PUBDB-2023-06458

Report No.: DESY-23-175; arXiv:2311.02742

Abstract: We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and mean-field behaviour. We use the Lorentzian inversion formula to compute infinitely many three-loop corrections in the two-dimensional LRI near the mean-field end. We further exploit the exact OPE relations that follow from bulk locality of the LRI to compute infinitely many two-loop corrections near the mean-field end, as well as some one-loop corrections near SRI. By including such exact OPE relations in the crossing equations for LRI we set up a very constrained bootstrap problem, which we solve numerically using SDPB. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI.

Keyword(s): dimension, 2 ; dimension, 3 ; numerical calculations, Monte Carlo ; bootstrap ; long-range ; operator product expansion ; critical phenomena ; short-range ; family ; Ising model ; kink ; perturbation theory ; crossing

Note: 49 + 13 pages, 10 figures, 1 ancillary notebook

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. FUNBOOTS - Solving Conformal Field Theories with the Functional Bootstrap (101043588) (101043588)
3. QFT.zip - Compressing many-body quantum states in continuous space-time with tensor networks (101040260) (101040260)
4. DFG project 400570283 - Das Conformal Bootstrap Programm (400570283) (400570283)
5. DFG project 471314740 - Holographie und das Swampland: Konsistenzbedingungen an fundamentale Physik aus der Quantengravitation (471314740) (471314740)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2023

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Database coverage:
; ; Published

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article Behan, C. ; Lauria, E. (Corresponding author) ; Nocchi, M. ; Vliet, P. J. v.DESY*
Analytic and numerical bootstrap for the long-range Ising model
Journal of high energy physics 2024(3), 136 (2024) [10.1007/JHEP03(2024)136]2024     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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