论文标题
在整个低温方向上，三维随机场Ising模型的远程顺序
Long range order for three-dimensional random field Ising model throughout the entire low temperature regime
论文作者
论文摘要
对于$ d \ geq 3 $，我们在$ \ mathbb z^d $上使用$ \ {εh_v：v \ in \ mathbb z^d \} $提供随机字段的ising模型，其中$ h_v $ h_v $是均值0和差异的独立正常变量，我们显示了$ t <t_c $。 $ε$足够小，具体取决于$ t $。我们的工作将Imbrie（1985）和Bricmont-Kupiainen（1988）的先前结果从非常低的温度状态扩展到整个低温状态。
For $d\geq 3$, we study the Ising model on $\mathbb Z^d$ with random field given by $\{εh_v: v\in \mathbb Z^d\}$ where $h_v$'s are independent normal variables with mean 0 and variance 1. We show that for any $T < T_c$ (here $T_c$ is the critical temperature without disorder), long range order exists as long as $ε$ is sufficiently small depending on $T$. Our work extends previous results of Imbrie (1985) and Bricmont--Kupiainen (1988) from the very low temperature regime to the entire low temperature regime.
