Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908497342365696 |
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| author | Affonso, Lucas Bissacot, Rodrigo Maia, João Rodrigues, João F. Welsch, Kelvyn |
| author_facet | Affonso, Lucas Bissacot, Rodrigo Maia, João Rodrigues, João F. Welsch, Kelvyn |
| contents | We develop the cluster expansion for the multidimensional multiscaled contours defined by three of us. These contours are suitable for long-range Ising models with interaction $J_{xy}=J(|x-y|)= J/|x-y|^α$, $J>0$, and $α>d$. As an application of the convergence of the cluster expansion at low temperatures, we study the decay of the truncated two-point correlation functions, showing that the decay is algebraic with coefficient $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models Affonso, Lucas Bissacot, Rodrigo Maia, João Rodrigues, João F. Welsch, Kelvyn Mathematical Physics Statistical Mechanics 82B05, 82B20 We develop the cluster expansion for the multidimensional multiscaled contours defined by three of us. These contours are suitable for long-range Ising models with interaction $J_{xy}=J(|x-y|)= J/|x-y|^α$, $J>0$, and $α>d$. As an application of the convergence of the cluster expansion at low temperatures, we study the decay of the truncated two-point correlation functions, showing that the decay is algebraic with coefficient $α$. |
| title | Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models |
| topic | Mathematical Physics Statistical Mechanics 82B05, 82B20 |
| url | https://arxiv.org/abs/2508.15666 |