Speaker: Jian Ding (Peking University)
Title: Recent progress on random field Ising model
Abstract: Random field Ising model is a canonical example to study the effect of disorder on long range order. In 70's, Imry-Ma predicted that in the presence of weak disorder, the long-range order persists at low temperatures in three dimensions and above but disappears in two dimensions. In this talk, I will review mathematical development surrounding this prediction, and I will focus on recent progress on exponential decay (joint with Jiaming Xia) and correlation length in dimension two (joint with Mateo Wirth), a new proof for long range order in dimension three (joint with Zijie Zhuang) and a recent general inequality for the Ising model (joint with Jian Song and Rongfeng Sun) which has implications for random field Ising model.