Hugo Duminil-Copin

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.