Analytic and numerical bootstrap for the long-range Ising model

Journal article

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.

Authors: Behan, C; Lauria, E; Nocchi, M; van Vliet, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2024
• Issue: 3
• Article number: 136
• Publication date: 2024-03-22
• Acceptance date: 2024-03-06
• DOI: 10.1007/jhep03(2024)136
• EISSN: 1029-8479
• Language: English
• Keywords: Renormalization Group; Nonperturbative Effects; Conformal and W Symmetry; Boundary Quantum Field Theory