Long range order for three-dimensional random field Ising model throughout the entire low temperature regime

地   点：  会议室(703)

报告人：  丁剑教授

单   位：  北京大学

邀请人：  张登

备   注：  Jian Ding is a professor at School of Mathematical Sciences, Peking University. His research interests are probability theory with focus on interactions with statistical physics, theory of computer science and combinatorial statistics. Before joining Peking University, he has been a postdoc at Stanford, and a faculty member at University of Chicago and University of Pennsylvania, after his Ph.D. at UC Berkeley in 2011.

报告摘要：  

Consider Ising model in three and higher dimensions with i.i.d. Gaussian externel field. We are going to show that for any temperature lower than the corresponding critical temperature without disorder (i.e. the external field), the model exhibits spontaneous magnetization as long as the magnitude of the disorder is sufficiently small. Our work extends previous results of Imbrie (1985) and Bricmont–Kupiainen (1988) (see also Ding-Zhuang (2021)) which treated the the zero and very low temperature cases respectively. This talk is based on a joint work (https://arxiv.org/abs/2209.13998) with Yu Liu and Aoteng Xia.