Critical Phenomena Through the Lens of the Ising Model by Hugo Duminil-Copin

Explore the fascinating world of critical phenomena through the lens of the Ising model in this illuminating lecture by Fields Medal recipient Hugo Duminil-Copin. Delve into the rich history and mathematical intricacies of this classical lattice model, originally conceived for ferromagnetism but now recognized as a powerful tool for understanding cooperative phenomena. Discover recent breakthroughs in three- and four-dimensional Ising models, focusing on a probabilistic interpretation that links them to percolation models. Gain insights into the model's critical phase, its applications in statistical physics, and its connections to Euclidean Field Theory. Learn about the scaling limits of spin fluctuations in four-dimensional Ising-type models and their implications for λϕ4 fields. Uncover the sophisticated mathematical techniques, including random current representation and multi-scale analysis, used to improve tree diagram bounds and analyze intersection probabilities.

Critical Phenomena Through the Lens of the Ising Model (Lecture 1) by Hugo Duminil-Copin