Analytic and numerical bootstrap for the long-range Ising model

Author(s)

Behan, Connor ; Lauria, Edoardo ; Nocchi, Maria ; van Vliet, Philine

• Document type: Journal article
• Source: Journal of High Energy Physics; v. N/A, n. 3, p. 62-pg., 2024-03-22.

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. (AU)

• FAPESP's process: 19/24277-8 - Applications of quantum field theory
• Grantee: Pedro Gil Martins Vieira
• Support Opportunities: Research Projects - SPEC Program
• FAPESP's process: 23/03825-2 - Scattering theory meets critical phenomena
• Grantee: Connor Classen Behan
• Support Opportunities: Scholarships in Brazil - Post-Doctoral