1d Long-range Ising Model Near the Short-range Crossover

by Philine van Vliet (LPTENS, École Normale Supérieure)

Wednesday Jul 9, 2025, 9:30 AM → 10:30 AM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Seed Seminar of Mathematics and Physics

One of the features of the critical behavior of the long-range Ising model (LRI) with interactions decaying as 1/r^s+d is that it has a line of interacting fixed points, and hence corresponds to an family of interacting d-dimensional CFT, for d/2 < s < s_∗. Both ends of this range of s admit a weakly-coupled description. For small s, the theory is described as a generalized free field with a φ⁴ interaction. For large s, the theory can be described by the d-dimensional short-range Ising model (SRI) coupled to a generalized free field. While these descriptions have been used to study the LRI in dimensions d > 1, in d = 1 it leads to a fascinating puzzle. The 1d LRI still has a line of interacting fixed points for 1/2 < s < 1. However, it is well-known that the SRI does not have a second-order phase transition in 1d and leaves the question what happens when s approaches . In this talk I will discuss our model which provides a weakly-coupled description for the 1d LRI around s = 1. At s = 1, our model becomes an exactly solvable conformal boundary condition for the 2d free scalar. We perform a number of consistency checks of our proposal and calculate CFT data around s = 1 using perturbation theory and the analytic bootstrap. This is based on https://arxiv.org/pdf/2412.12243.

 

========

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe seminaire_mathematique PRENOM NOM"
(indiquez vos propres prénom et nom) et laissez le corps du message vide.