Analytic and numerical bootstrap for the long-range Ising model

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Main Authors: Behan, Connor, Lauria, Edoardo, Nocchi, Maria, van Vliet, Philine
Format: Preprint
Published: 2023
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author Behan, Connor
Lauria, Edoardo
Nocchi, Maria
van Vliet, Philine
author_facet Behan, Connor
Lauria, Edoardo
Nocchi, Maria
van Vliet, Philine
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_02742
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Analytic and numerical bootstrap for the long-range Ising model
Behan, Connor
Lauria, Edoardo
Nocchi, Maria
van Vliet, Philine
High Energy Physics - Theory
Statistical Mechanics
Strongly Correlated Electrons
High Energy Physics - Lattice
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.
title Analytic and numerical bootstrap for the long-range Ising model
topic High Energy Physics - Theory
Statistical Mechanics
Strongly Correlated Electrons
High Energy Physics - Lattice
url https://arxiv.org/abs/2311.02742