We study the random field Ising model on $${\mathbb {Z}}^2$$ Z 2 where the external field is given by i.i.d. Gaussian variables with mean zero and positive variance. We show that the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary.

中文翻译：

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二维随机场 Ising 模型中相关性的指数衰减

我们研究了 $${\mathbb {Z}}^2$$ Z 2 上的随机场 Ising 模型，其中外部场由具有均值零和正方差的 iid 高斯变量给出。我们表明，边界条件对有限盒子中磁化强度的影响在到边界的距离上呈指数衰减。