The Lee-Yang property of isotropic vector ferromagnets and lattice fields
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908900898373632 |
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| author | Kozitsky, Yuri |
| author_facet | Kozitsky, Yuri |
| contents | The Lee-Yang property of a given spin model means that its partition function has purely imaginary zeros as a function of an external magnetic field. A similar property is also used in the theory of quantum anharmonic crystals and quantum lattice fields. A number of powerful analytic methods of the mathematical theory of such models employ this property. Its suitable generalization is used in the theory of models of isotropic $D$-dimensional spins (rotors) or $D$-component quantum lattice fields. So far, the (generalized) Lee-Yang property has been established only for two-dimensional isotropic models. In this work, we prove that isotropic spin and field models living on $\mathds{Z}$ have this property for all even $D$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18675 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Lee-Yang property of isotropic vector ferromagnets and lattice fields Kozitsky, Yuri Mathematical Physics 82B20, 81T18, 30C15, 32A15 The Lee-Yang property of a given spin model means that its partition function has purely imaginary zeros as a function of an external magnetic field. A similar property is also used in the theory of quantum anharmonic crystals and quantum lattice fields. A number of powerful analytic methods of the mathematical theory of such models employ this property. Its suitable generalization is used in the theory of models of isotropic $D$-dimensional spins (rotors) or $D$-component quantum lattice fields. So far, the (generalized) Lee-Yang property has been established only for two-dimensional isotropic models. In this work, we prove that isotropic spin and field models living on $\mathds{Z}$ have this property for all even $D$. |
| title | The Lee-Yang property of isotropic vector ferromagnets and lattice fields |
| topic | Mathematical Physics 82B20, 81T18, 30C15, 32A15 |
| url | https://arxiv.org/abs/2603.18675 |