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arXiv · 2609.19005

The Thermodynamic Limit of Short-Range Spin Glasses with Periodic Boundary Conditions

Hexiang Wang·Keheng Zhu·Mauris Chueng
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Abstract

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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Hexiang Wang, Keheng Zhu, Mauris Chueng. 2026-07-18. The Thermodynamic Limit of Short-Range Spin Glasses with Periodic Boundary Conditions. https://arxiv.org/abs/2609.19005

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