Analytic and numerical bootstrap for the long-range Ising model

• Main Author: Behan, Connor [UNESP]
• Publication Date: 2024
• Other Authors: Lauria, Edoardo, Nocchi, Maria, van Vliet, Philine
• Format: Article
• Language: eng
• Source: Repositório Institucional da UNESP
• Download full: http://dx.doi.org/10.1007/JHEP03(2024)136; https://hdl.handle.net/11449/304109
• topic: Boundary Quantum Field Theory; Conformal and W Symmetry; Nonperturbative Effects; Renormalization Group

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.