Exponential decay of correlations at high temperature in $H^{2|2n}$ nonlinear sigma models
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866911548027437056 |
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| author | Disertori, Margherita Fernández, Javier Durán Fresta, Luca |
| author_facet | Disertori, Margherita Fernández, Javier Durán Fresta, Luca |
| contents | We consider a family of nonlinear sigma models on $\mathbb{Z}^{d}$ whose target space is the hyperbolic super manifold $H^{2|2n}$, $n >1$, introduced by Crawford as an extension of Zirnbauer's $H^{2|2}$ model for disordered systems. We prove exponential decay of the two-point correlation function in the high-temperature regime $β\leq C n^{-1}$, with $C>0$ a universal constant, for any $n>1$ and any dimension $d\geq 1$, with mass $\log β^{-1}$. We also consider models with long-range interaction and prove fast decay in the same high-temperature regime. The proof is based on the reduction to a marginal fermionic theory and combines a high-temperature cluster expansion, exact combinatorics and bounds derived via Grassmann norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26157 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exponential decay of correlations at high temperature in $H^{2|2n}$ nonlinear sigma models Disertori, Margherita Fernández, Javier Durán Fresta, Luca Mathematical Physics Probability We consider a family of nonlinear sigma models on $\mathbb{Z}^{d}$ whose target space is the hyperbolic super manifold $H^{2|2n}$, $n >1$, introduced by Crawford as an extension of Zirnbauer's $H^{2|2}$ model for disordered systems. We prove exponential decay of the two-point correlation function in the high-temperature regime $β\leq C n^{-1}$, with $C>0$ a universal constant, for any $n>1$ and any dimension $d\geq 1$, with mass $\log β^{-1}$. We also consider models with long-range interaction and prove fast decay in the same high-temperature regime. The proof is based on the reduction to a marginal fermionic theory and combines a high-temperature cluster expansion, exact combinatorics and bounds derived via Grassmann norms. |
| title | Exponential decay of correlations at high temperature in $H^{2|2n}$ nonlinear sigma models |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2603.26157 |