Hugo Duminil-Copin
University of Geneva and Institut des Hautes Études Scientifiques, Paris
Date
17 April 2024
Host
Gian Michele Graf
Title
Scaling Limits and Field Theory Implications for Critical 4D Ising and ϕ44 Models
Abstract
In this presentation, we delve into the nuanced intricacies surrounding the scaling limits of spin fluctuations within four-dimensional Ising-type models, specifically those with nearest-neighbor ferromagnetic interactions near the critical point. More precisely, we prove Gaussian behavior and its implications within the realm of Euclidean Field Theory. The foundation of our proof lies in the innovative random current representation of these models, revealing the deviation of correlation functions from Wick‘s law in terms of intersection probabilities of random currents with sources at distances significantly larger than the model‘s lattice scale. Drawing inspiration from random walk intersection amplitudes, our analysis hones in on refining certain diagram bounds, introducing a logarithmic correction term through meticulous multi-scale analysis.
Recording
ETH Video Portal
