Marginal triviality of the scaling limits of 4D critical Ising and $\varphi^4_4$ models

Abstract: The talk will outline the recent proof that the scaling limits of spin fluctuations in four-dimensional Ising-type models at or near the critical point are Gaussian, and of the similar statement for the $\varphi^4_4$ fields with a lattice ultraviolet cutoff, in the limit of infinite volume and vanishing lattice spacing (derived jointly with H. Duminil-Copin). The proofs are enabled by the models' random current representation, in which the correlation functions' deviation from Wick's law are expressed in terms of intersection probabilities of random currents with prescribed sources. Examples will also be provided of insights facilitated by this representation for two and three dimensions.

other condensed mattersoft condensed matterstatistical mechanicsstrongly correlated electronssuperconductivitygeneral relativity and quantum cosmologyHEP - theorymathematical physicschaotic dynamicsfluid dynamicsquantum physics

Audience: researchers in the topic

Kadanoff seminars