无序Edwards--Anderson模型中的切向表面压力与边界局域化
Tangential Surface Pressures and Boundary Localization in Disordered Edwards--Anderson Models
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中文总结 AI 辅助
本研究证明无序Edwards--Anderson模型中切向边界自由能修正的收敛性，并通过均匀指数边界混合条件建立具有显式指数速率的边界局域化，推广至所有维度及对称耦合律。
中文摘要 AI 辅助
我们研究无序Edwards--Anderson伊辛模型中的边界自由能。对于固定宽度的矩形条带，我们证明期望的自由-固定边界修正除以切向长度，在每一个有限逆温度和零温度下都收敛。证明结合了均匀近可加性估计与乘积测度集中性，从而沿切向区间获得自平均性。我们推导出一个精确的有限体积高斯插值恒等式，并证明均匀指数边界混合条件蕴含具有显式指数速率的边界局域化。切向压力定理推广到所有维度和具有有限一阶矩的对称耦合律；在乘积集中性假设下，沿切向立方体获得自平均性。最后，一个次临界开键判据（对稀疏符号耦合显式验证）在无需假设无限体积吉布斯态性质的情况下给出低温局域化。
英文摘要
We study boundary free energies in disordered Edwards--Anderson Ising models. For rectangular strips of fixed width, we prove that the expected free-to-fixed boundary correction, divided by the tangential length, converges for every finite inverse temperature and at zero temperature. The proof combines a uniform almost-additivity estimate with product-measure concentration, yielding self-averaging along tangential intervals. We derive an exact finite-volume Gaussian interpolation identity and prove that a uniform exponential boundary-mixing condition implies boundary localization with an explicit exponential rate. The tangential pressure theorem extends to all dimensions and symmetric coupling laws with finite first moment; under a product-concentration hypothesis, self-averaging is obtained along tangential cubes. Finally, a subcritical open-bond criterion, verified explicitly for sparse signed couplings, gives low-temperature localization without assuming an infinite-volume Gibbs-state property.
