Stochastik

The 2d (massless) Sinh-Gordon model is amongst the simplest 2d quantum field theories that are expected to be integrable (= infinitely many symmetries), but without conformal symmetry. In this talk I will explain a rigorous construction of this model and its vertex correlations (= Laplace transforms) on the infinite cylinder using probability theory. In particular, I will explain how the theory of Gaussian multiplicative chaos can be used to analyze the spectrum of the corresponding Sinh-Gordon Hamiltonian. This talk will be based on joint work with Colin Guillarmou and Vincent Vargas.

We study the (discrete) Phi^4 model on Z^d with algebraically decaying long-range interactions. This model is the natural discrete analogue of the fractional continuous Phi^4 model. We first describe some general properties of the phase transition that the model undergoes. Then, we study the nature of the critical scaling limits of the model, proving in particular the (marginal) triviality of these limits in dimension 3 with well-chosen interactions.