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.

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

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• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Universality in long-range interacting systems: the effective dimension approach
• Casimir Forces in CFT with Defects and Boundaries
• 1d Ising model with $1/r^{1.99}$ interaction
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Addendum: Long-range multi-scalar models at three loops
• Dynamic critical exponent in quantum long-range models
• RG studies of scalar-field models of long-range interactions
• One-dimensional long-range Ising model: two (almost) equivalent approximations