MARK KAC SEMINAR

A statistical mechanics system at a second order phase transition is characterized by a set of critical exponents describing the behavior of a few key physical quantities at or close to the transition, such as the order parameter (e.g. the magnetization in the Ising model), the correlation length, the susceptibility, or the polynomial decay of correlations of local fluctuations. These critical exponents are believed to be robust under a large class of perturbations of the microscopic Hamiltonian used to model the system, and to characterize uniquely the Euclidean field theory describing the large distance behavior of correlations. It is widely expected that this field theory is conformally invariant and can be constructed as the fixed point of a Wilsonian Renormalization Group (RG) transformation. Mathematically, there are very few cases where these expectations can be rigorously substantiated, particularly if we restric our attention to cases where the limiting Euclidean field theory is non-trivial, i.e., non-Gaussian. In this seminar I will introduce a three dimensional model of self-interacting fermions admitting a non-Gaussian RG fixed point, for which many such properties can be rigorously proven. I will describe the construction of the limiting Euclidean field theory, of the robustness of its critical exponents, and I will outline a program for proving its conformal invariance. Talks based on joint works with Vieri Mastropietro, Slava Rychkov and Giuseppe Scola.