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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.12033 |
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| _version_ | 1866910051403300864 |
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| author | Chen, Hong-Bin Issa, Victor |
| author_facet | Chen, Hong-Bin Issa, Victor |
| contents | This paper constitutes the first part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part.
In this paper, we focus on models whose spin glass part satisfies the usual convexity assumption. We identify the limit free energy via a Parisi-type formula and prove a large deviation principle for the mean magnetization. The proof is remarkably simple and short compared to previous approaches; it relies on treating the Mattis interaction as a parameter of the model.
In the companion paper, we establish similar results in the high-temperature regime for models whose spin glass part is not assumed to satisfy the usual convexity assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12033 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vector spin glasses with Mattis interaction I: the convex case Chen, Hong-Bin Issa, Victor Probability Disordered Systems and Neural Networks 82B44, 60F10, 35F21 This paper constitutes the first part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on models whose spin glass part satisfies the usual convexity assumption. We identify the limit free energy via a Parisi-type formula and prove a large deviation principle for the mean magnetization. The proof is remarkably simple and short compared to previous approaches; it relies on treating the Mattis interaction as a parameter of the model. In the companion paper, we establish similar results in the high-temperature regime for models whose spin glass part is not assumed to satisfy the usual convexity assumption. |
| title | Vector spin glasses with Mattis interaction I: the convex case |
| topic | Probability Disordered Systems and Neural Networks 82B44, 60F10, 35F21 |
| url | https://arxiv.org/abs/2603.12033 |