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PreprintarXiv licencearXiv

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|<∞, 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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Cite

BibTeXRIS
BibTeX
@misc{wang2026thermodynamic,
  title = {{The Thermodynamic Limit of Short-Range Spin Glasses with Periodic Boundary Conditions}},
  author = {Hexiang Wang and Keheng Zhu and Mauris Chueng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19005},
  eprint = {2609.19005},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19005},
}
RIS
TY  - UNPB
TI  - The Thermodynamic Limit of Short-Range Spin Glasses with Periodic Boundary Conditions
AU  - Hexiang Wang
AU  - Keheng Zhu
AU  - Mauris Chueng
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.19005
UR  - https://arxiv.org/abs/2609.19005
AB  - 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|<∞, 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.
ER  -