报告题目：Random Field Ising Model: Off Critical and Near Critical Behavior
时 间：2024年1月24日（星期三）9：00
地 点：科研楼18号楼1102
主 办：数学与统计学院
参加对象：概率统计系及其他感兴趣的师生
报告摘要：We studied the random field Ising model(RFIM) on the box [-N,N]^d\cap Z^d with external field {\epsilon h_v} where h_v will be i.i.d. normal variables. Our main interest is the behavior boundary influence m(T,N,\epsilon). In dimension d\geq 3, we proved that for any T<T_c and \epsilon fixed but small enough, m(T,N,\epsilon) has a positive lower bound as N goes to infinity. In dimension 2, it has been proved that m(T,N,\epsilon) decay to 0 with exponential rate for any temperature T and any \epsilon>0 fixed. And we focus on the critical temperature T_c and the case that \epsilon decays with N. The main result is that if \epsilon<<N^{-7/8} it has little influence, i.e., m(T_c,N,\epsilon) has the same order with m(T_c,N,0); if \epsilon>>N^{-7/8}, the ratio between m(T_c,N,\epsilon) and m(T_c,N,0) will be of order exp(-c\epsilon^{8/7}N). This talk is based on two joint works with Jian Ding, Fenglin Huang, Yu Liu.
报告人简介： 夏傲腾：北京大学数学科学学院博士，指导老师为李欣意老师。在带有外场的Ising 模型性质上做了重要工作。