Fluctuations in the non-linear supersymmetric hyperbolic sigma model with long-range interactions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910566617972736 |
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| author | Disertori, Margherita Merkl, Franz Rolles, Silke W. W. |
| author_facet | Disertori, Margherita Merkl, Franz Rolles, Silke W. W. |
| contents | We consider a class of non-linear supersymmetric hyperbolic sigma models with long-range interactions on boxes in $\mathbb{Z}^d$ and on a hierarchical lattice. We prove that the random field associated to a marginal in horospherical coordinates has asymptotically arbitrarily small fluctuations for large enough interactions, uniformly in the size of the boxes. This can be viewed as a strong version of spontaneous breaking of the Lorentz boost symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08136 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fluctuations in the non-linear supersymmetric hyperbolic sigma model with long-range interactions Disertori, Margherita Merkl, Franz Rolles, Silke W. W. Mathematical Physics Probability Primary 82B20, secondary 60G60 We consider a class of non-linear supersymmetric hyperbolic sigma models with long-range interactions on boxes in $\mathbb{Z}^d$ and on a hierarchical lattice. We prove that the random field associated to a marginal in horospherical coordinates has asymptotically arbitrarily small fluctuations for large enough interactions, uniformly in the size of the boxes. This can be viewed as a strong version of spontaneous breaking of the Lorentz boost symmetry. |
| title | Fluctuations in the non-linear supersymmetric hyperbolic sigma model with long-range interactions |
| topic | Mathematical Physics Probability Primary 82B20, secondary 60G60 |
| url | https://arxiv.org/abs/2408.08136 |