Analytic and numerical bootstrap for the long-range Ising model
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.
Keywords
Cite
@article{arxiv.2311.02742,
title = {Analytic and numerical bootstrap for the long-range Ising model},
author = {Connor Behan and Edoardo Lauria and Maria Nocchi and Philine van Vliet},
journal= {arXiv preprint arXiv:2311.02742},
year = {2025}
}
Comments
71 + pages, 11 figures, 1 ancillary notebook. v4: updated three-loop results from 2411.00805. v5: fixed typo in eq. (3.10) and added a reference, v6: fixed typo in appendix B