论文标题
通过贪婪的晶格动物的二维随机场Ising模型的相关长度
Correlation length of the two-dimensional random field Ising model via greedy lattice animal
论文作者
论文摘要
对于二维随机场ISING模型，随机场由I.I.D. \ \均值零高斯变量具有方差$ε^2 $给出，我们研究（一个自然概念）相关长度，这是一个盒子的关键大小，该盒子的关键大小是随机场的影响以及自旋磁力的边界条件的影响。我们表明，作为$ε\至0 $，在零温度下，相关长度缩放为$ e^{θ（ε^{ - 4/3}）} $（并且我们的上限适用于所有正温度）。
For the two-dimensional random field Ising model where the random field is given by i.i.d.\ mean zero Gaussian variables with variance $ε^2$, we study (one natural notion of) the correlation length, which is the critical size of a box at which the influences of the random field and of the boundary condition on the spin magnetization are comparable. We show that as $ε\to 0$, at zero temperature the correlation length scales as $e^{Θ(ε^{-4/3})}$ (and our upper bound applies for all positive temperatures).
