AI 中文总结
该研究针对无序伊辛模型，证明了固定深度切向压力存在、吉布斯态选择独立性等结论，建立了全表面极限并给出反例，为相关统计物理问题提供了理论支撑。
AI 中文摘要
我们研究最近邻无序伊辛模型中的边界自由能与半空间响应。首先，证明固定深度切向压力的存在性，并确定其导数几乎处处与极限边界响应相等；其次，在淬火指数边界响应混合条件下，证明吉布斯态选择的独立性及有限深度压力的指数收敛性，进一步表明均匀单自旋混合可得到DLR唯一性与高斯正态局域化，并在(2d-1)E[tanh(β|J|)]<1时验证所需混合条件；最后，在有界Dobrushin区域建立全表面极限，并提供反例界定一般表面与刚度断言的适用范围。
英文摘要
We study boundary free energies and half-space responses in nearest-neighbor disordered Ising models. First, we prove the existence of fixed-depth tangential pressure and identify its derivative almost everywhere with the limiting boundary response. Second, under quenched exponential boundary-response mixing, we prove Gibbs-state selection independence and exponential convergence of finite-depth pressures. We further show that uniform one-spin mixing yields DLR uniqueness and Gaussian normal localization, and verify the required mixing conditions whenever $(2d-1)\mathbb E\tanh(β\vert{}J\vert{})<1$. Finally, we establish an all-face surface limit in the bounded Dobrushin regime and provide counterexamples that delimit general surface and stiffness claims.
Comments33 pages, 2 figures
