Emergence of fractional Gaussian free field correlations in subcritical long-range Ising models
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911767116906496 |
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| author | Gunaratnam, Trishen S. Panis, Romain |
| author_facet | Gunaratnam, Trishen S. Panis, Romain |
| contents | We study corrections to the scaling limit of subcritical long-range Ising models with (super)-summable interactions on $\mathbb{Z}^d$. For a wide class of models, the scaling limit is known to be white noise, as shown by Newman (1980). In the specific case of couplings $J_{x,y}=|x-y|^{-d-\boldsymbolα}$, where $\boldsymbolα>0$ and $|\cdot|$ is the Euclidean norm, we find an emergence of fractional Gaussian free field correlations in appropriately renormalised and rescaled observables. The proof exploits the exact asymptotics of the two-point function, first established by Newman and Spohn (1998), together with the rotational symmetry of the interaction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11887 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Emergence of fractional Gaussian free field correlations in subcritical long-range Ising models Gunaratnam, Trishen S. Panis, Romain Probability Mathematical Physics 82B20, 60G60, 60K35 We study corrections to the scaling limit of subcritical long-range Ising models with (super)-summable interactions on $\mathbb{Z}^d$. For a wide class of models, the scaling limit is known to be white noise, as shown by Newman (1980). In the specific case of couplings $J_{x,y}=|x-y|^{-d-\boldsymbolα}$, where $\boldsymbolα>0$ and $|\cdot|$ is the Euclidean norm, we find an emergence of fractional Gaussian free field correlations in appropriately renormalised and rescaled observables. The proof exploits the exact asymptotics of the two-point function, first established by Newman and Spohn (1998), together with the rotational symmetry of the interaction. |
| title | Emergence of fractional Gaussian free field correlations in subcritical long-range Ising models |
| topic | Probability Mathematical Physics 82B20, 60G60, 60K35 |
| url | https://arxiv.org/abs/2306.11887 |