论文标题
二维随机场模型的相关长度的上限和下限
Upper and Lower Bounds for the Correlation Length of the Two-Dimensional Random-Field Ising Model
论文作者
论文摘要
我们研究了弱场强度$ \ varepsilon $的二维随机场ISING模型中的相关衰减速率。我们将相关性衰减的证据的元素与艾森曼（Aizenman）的结果进行定量改进，以随机曲线的曲折性上的曲折性获得，以获得$ \ exp（\ exp（o（1/\ varepsilon^{2}}} {2}} {2}}））的上限（\ exp exp（o（1/\ varepsilon^{2}}}）））$上的相关长度。相反，我们通过适应Fisher-fröhlich-spencer的方法来表明，在侧面长度的正方形域上，$ \ exp（o（1/\ varepsilon^{2/3}}））$该模型继续表现出低温下边界条件的强烈依赖。
We study the rate of correlation decay in the two-dimensional random-field Ising model at weak field strength $\varepsilon$. We combine elements of the recent proof of exponential decay of correlations with a quantitative refinement of a result of Aizenman--Burchard on the tortuosity of random curves to obtain an upper bound of the form $\exp(\exp(O(1/\varepsilon^{2})))$ on the correlation length of the model at all temperatures. Conversely, we show, by adapting methods of Fisher--Fröhlich--Spencer, that on square domains of side length as large as $\exp(O(1/\varepsilon^{2/3}))$ the model continues to exhibit strong dependence on boundary conditions at low temperature.
