AI 中文总结
本文证明周期边界条件下最近邻Edwards-Anderson Ising模型在离散环面上的淬火热力学极限存在，且自由能密度几乎必然自平均，仅需有限一阶矩假设，并给出有限体积修正的定量界。
AI 中文摘要
对于离散环面上的最近邻Edwards--Anderson Ising模型，我们证明了淬火热力学极限的存在性以及自由能密度的几乎必然自平均性。主要论证中唯一的矩假设是$\E|J|<\infty$，且不需要耦合定律的对称性或中心化。证明避免了周期次可加性：环绕键构成表面阶扰动，而平铺论证和强大数定律给出了自由边界极限。我们还获得了无序平均有限体积修正的定量界$(O(L^{-1})$。由于跨体积的几乎必然陈述否则无法良好定义，我们指定了一个精确的公共概率空间。
英文摘要
For the nearest-neighbour Edwards--Anderson Ising model on the discrete torus, we prove existence of the quenched thermodynamic limit and almost-sure self-averaging of the free-energy density. The only moment assumption in the main argument is $\E|J|<\infty$, and no symmetry or centering of the coupling law is needed. The proof avoids periodic subadditivity: the wrap-around bonds form a surface-order perturbation, while a tiling argument and the strong law of large numbers give the free-boundary limit. We also obtain the quantitative bounds $(O(L^{-1})$ for the disorder-averaged finite-volume correction. A precise common probability space is specified, since an almost-sure statement across volumes is otherwise not well defined.
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