AI 中文总结
研究短程Edwards-Anderson伊辛模型在立方盒上的随机边界扰动，证明能量包络与体积相比可忽略的扰动不改变极限淬火比自由能，验证了相关假设，结果涉及比自由能，不涉及有限体积吉布斯测度收敛。
AI 中文摘要
我们考虑在立方盒上具有在边界处支持的随机扰动的最近邻Edwards-Anderson伊辛模型。我们证明，任何在期望和几乎必然意义下，其能量包络与体积相比可忽略不计的扰动，都不会改变极限淬火比自由能。对于至少二维的独立有限方差体无序，Efron-Stein估计也能得到沿整个盒序列的几乎必然自平均性。我们验证了独立同分布标量表面场、固定随机外部自旋和周期性环绕键的假设，淬火均值的比较为\(O(L^{-1})\)。该结果涉及比自由能，并不断言有限体积吉布斯测度的收敛性。
英文摘要
We consider the nearest-neighbor Edwards--Anderson Ising model on cubic boxes with random perturbations supported at the boundary. We prove that any perturbation admitting an energy envelope that is negligible compared with the volume, both in expectation and almost surely, leaves the limiting quenched specific free energy unchanged. For independent finite-variance bulk disorder in dimension at least two, an Efron--Stein estimate also yields almost-sure self-averaging along the full sequence of boxes. The hypotheses are verified for i.i.d. scalar surface fields, fixed random exterior spins, and periodic wrap-around bonds, with an $ O(L^{-1}) $ comparison of quenched means. The result concerns the specific free energy and does not assert convergence of finite-volume Gibbs measures.
Comments10 pages,4 fugeres
