Probability Seminar —— Decay of Correlations for Long range Ising models at low temperatures
报告人：Lucas Affonso (University of São Paulo and NYU Shanghai)
时间：2026-04-27 15:00-16:00
地点：四元厅
Abstract: Long-range Ising systems display phase coexistence and correlation decay behaviors that are markedly different from those in finite-range models, and remain comparatively less understood. In this talk, I will discuss recent results for ferromagnetic Ising models with interactions of the form \(J_{xy} \sim |x-y|^{-\alpha}\), with \(\alpha > d\), focusing on the decay of truncated two-point correlations at low temperatures. The main ingredient is a multiscale contour framework, designed to effectively treat long-range interactions, combined with a cluster expansion tailored to this setting. I will explain how these methods yield algebraic decay of correlations, with exponents governed by the interaction, and comment on further contexts where contour techniques may be applicable.
Bio: Lucas Affonso is a postdoctoral researcher at IME-USP, Brazil. He is currently a visiting postdoctoral fellow at NYU-Shanghai under the supervision of Roberto Fernández. His research interests lie in equilibrium classical and quantum statistical mechanics, with a particular focus on systems with long range interactions.
