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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.03510 |
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| _version_ | 1866917967686533120 |
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| author | Kozitsky, Yuri |
| author_facet | Kozitsky, Yuri |
| contents | According to the Lieb-Sokal theorem, the partition function, $Z$, of a ferromagnetic spin model has the Lee-Yang property if the single-spin partition function has it. In this note, it is shown that for some spin models a ferromagnetic interaction can induce the Lee-Yang property of $Z$ even if the single-spin partition function fails to have it. In particular, this holds for the Blume-Capel model and for the annealed states of the $s=\pm 1$ site dilute Ising model with a neares-neighbor interaction on $\mathds{Z}^d$, as well as with interactions defined by a hierarchical structure similar to that of Dyson's hierarchical model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Lee-Yang property of some ferromagnets Kozitsky, Yuri Mathematical Physics 82B20, 82B27, 30D15 According to the Lieb-Sokal theorem, the partition function, $Z$, of a ferromagnetic spin model has the Lee-Yang property if the single-spin partition function has it. In this note, it is shown that for some spin models a ferromagnetic interaction can induce the Lee-Yang property of $Z$ even if the single-spin partition function fails to have it. In particular, this holds for the Blume-Capel model and for the annealed states of the $s=\pm 1$ site dilute Ising model with a neares-neighbor interaction on $\mathds{Z}^d$, as well as with interactions defined by a hierarchical structure similar to that of Dyson's hierarchical model. |
| title | On the Lee-Yang property of some ferromagnets |
| topic | Mathematical Physics 82B20, 82B27, 30D15 |
| url | https://arxiv.org/abs/2503.03510 |