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arXiv · 2507.11445

The stability of long-range order in disordered systems: A generalized Ding-Zhuang argument

Yejia Chen·Jianwen Zhou·Ruifeng Liu·Hai-Jun Zhou
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Abstract

The stability of long-range order against quenched disorder is a central problem in statistical mechanics. This paper develops a generalized framework extending the Ding-Zhuang method and integrated with the Pirogov-Sinai framework, establishing a systematic scheme for studying phase transitions of long-range order in disordered systems. We axiomatize the Ding-Zhuang approach into a theoretical framework consisting of the Peierls condition and a local symmetry condition. For systems in dimensions $d \geq 3$ satisfying these conditions, we prove the persistence of long-range order at low temperatures and under weak disorder, with multiple coexisting distinct Gibbs states. The framework's versatility is demonstrated for diverse models, providing a systematic extension of Peierls methods to disordered systems.

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Yejia Chen, Jianwen Zhou, Ruifeng Liu, Hai-Jun Zhou. 2025-07-15. The stability of long-range order in disordered systems: A generalized Ding-Zhuang argument. https://arxiv.org/abs/2507.11445

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