Continuous eigenfunctions of the transfer operator for Dyson models
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910919536148480 |
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| author | Johansson, Anders Öberg, Anders Pollicott, Mark |
| author_facet | Johansson, Anders Öberg, Anders Pollicott, Mark |
| contents | In this article we address a well known problem at the intersection of ergodic theory and statistical mechanics.
We prove that there exists a continuous eigenfunction for the transfer
operator corresponding to pair potentials that satisfy a square summability
condition on the variations, when the inverse temperature is subcritical. As a corollary we
obtain a continuous eigenfunction for the classical Dyson model, with
interactions $\J(k)=β\, k^{-α}$, $k\ge1$, in the whole subcritical
regime $β<β_c$ for which the parameter $α$ is greater than $3/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04202 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Continuous eigenfunctions of the transfer operator for Dyson models Johansson, Anders Öberg, Anders Pollicott, Mark Dynamical Systems Mathematical Physics 37D35, 37A60, 82B20, 82B26, 82C27 In this article we address a well known problem at the intersection of ergodic theory and statistical mechanics. We prove that there exists a continuous eigenfunction for the transfer operator corresponding to pair potentials that satisfy a square summability condition on the variations, when the inverse temperature is subcritical. As a corollary we obtain a continuous eigenfunction for the classical Dyson model, with interactions $\J(k)=β\, k^{-α}$, $k\ge1$, in the whole subcritical regime $β<β_c$ for which the parameter $α$ is greater than $3/2$. |
| title | Continuous eigenfunctions of the transfer operator for Dyson models |
| topic | Dynamical Systems Mathematical Physics 37D35, 37A60, 82B20, 82B26, 82C27 |
| url | https://arxiv.org/abs/2304.04202 |