Yu Liu, Jian Ding, Aoteng Xia: Long range order for three-dimensional random field Ising model throughout the entire low temperature regime


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 Jian Ding.


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