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Résumé |
I will discuss the classical 1d Ising model with long-range interactions decaying as 1/r^{q}. When 1 < q < 2, this model exhibits a second-order phase transition, described by a family of 1d CFTs. When 3/2 < q < 2, these CFTs are interacting and are perhaps the simplest CFTs not yet solved analytically.
It has been a longstanding open problem to solve the critical dynamics near q=2. In my talk, I will resolve it by introducing a new continuum decription of the model, in terms of fractional Brownian motion coupled to a two-level system. At q=2, the new description is equivalent to a boundary condition for the 2d free scalar, and is weakly coupled near q=2. It enables us to compute a wealth of CFT data, both using the field theory, and the analytic conformal bootstrap. |
