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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.11445 |
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| _version_ | 1866915391196889088 |
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| author | Chen, Yejia Zhou, Jianwen Liu, Ruifeng Zhou, Hai-Jun |
| author_facet | Chen, Yejia Zhou, Jianwen Liu, Ruifeng Zhou, Hai-Jun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The stability of long-range order in disordered systems: A generalized Ding-Zhuang argument Chen, Yejia Zhou, Jianwen Liu, Ruifeng Zhou, Hai-Jun Mathematical Physics Disordered Systems and Neural Networks Statistical Mechanics Probability 82B44, 60K35, 82B26, 82B20 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. |
| title | The stability of long-range order in disordered systems: A generalized Ding-Zhuang argument |
| topic | Mathematical Physics Disordered Systems and Neural Networks Statistical Mechanics Probability 82B44, 60K35, 82B26, 82B20 |
| url | https://arxiv.org/abs/2507.11445 |