Translation-invariant extreme Gibbs measures for the Blume–Capel model with a wand on a Cayley tree
UDC 517.98 We study the translation-invariant Gibbs measures for the Blume–Capel model with a wand on a Cayley tree of order $k.$  We find the exact critical value $\theta_{cr}=1$ such that there exists a unique translation-invariant Gibbs measure for $\theta \geq\theta_{cr}$ and there...
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| Datum: | 2020 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2281 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.98
We study the translation-invariant Gibbs measures for the Blume–Capel model with a wand on a Cayley tree of order $k.$  We find the exact critical value $\theta_{cr}=1$ such that there exists a unique translation-invariant Gibbs measure for $\theta \geq\theta_{cr}$ and there exist exactly three translation-invariant Gibbs measures for $0<\theta<\theta_{cr}$ in the case of a wand for the model.  In addition, we investigate the problem of (non)extremes for these measures. |
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| DOI: | 10.37863/umzh.v72i4.2281 |