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

Jian Ding, Yu Liu, Aoteng Xia

For $d\ge 3$, we study the Ising model on ${\mathbb{Z}}^d$ with random field given by $\{\epsilon h_v:v\in {\mathbb{Z}}^d\}$ where $h_v$'s are independent normal variables with mean 0 and vari…