"Bootstrapping the long-range Ising model"
Philine van Vliet
Lundi 22/01/2024, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
While the short-range Ising model has been solved exactly in 2d and has been studied to high precision in 3d, its long-range cousin, the long-range Ising model (LRI), has remained more mysterious. Nevertheless, the LRI forms a natural starting point for the study of nonlocal CFTs, and it can be analyzed using a variety of techniques, including the conformal bootstrap.
In this talk I will show results for the critical point of the LRI in two and three dimensions, where we interpret the LRI as a conformal defect in an auxiliary, free scalar bulk CFT. I will discuss three different and complementary approaches: perturbation theory, the analytic bootstrap, and the numerical bootstrap. A central role is played by relations between OPE coefficients, which allow us to gain an order in perturbation theory, and provide us with more stringent constraints when implemented in the numerical bootstrap. I will show kinks in both 2d and 3d, and compare them with perturbative results and Monte Carlo predictions.