%0 Electronic Article
%A Behan, Connor
%A Lauria, Edoardo
%A Nocchi, Maria
%A van Vliet, Philine
%T Analytic and numerical bootstrap for the long-range Ising model
%N DESY-23-175
%M PUBDB-2023-06458
%M DESY-23-175
%M arXiv:2311.02742
%D 2023
%Z 49 + 13 pages, 10 figures, 1 ancillary notebook
%X 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.
%K dimension, 2 (INSPIRE)
%K dimension, 3 (INSPIRE)
%K numerical calculations, Monte Carlo (INSPIRE)
%K bootstrap (INSPIRE)
%K long-range (INSPIRE)
%K operator product expansion (INSPIRE)
%K critical phenomena (INSPIRE)
%K short-range (INSPIRE)
%K family (INSPIRE)
%K Ising model (INSPIRE)
%K kink (INSPIRE)
%K perturbation theory (INSPIRE)
%K crossing (INSPIRE)
%F PUB:(DE-HGF)25
%9 Preprint
%R 10.3204/PUBDB-2023-06458
%U https://bib-pubdb1.desy.de/record/597168