Phase Transition in Long-Range $q-$state Models via Contours. Clock and Potts Models with Fields
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| Format: | Preprint |
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2024
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| _version_ | 1866914030942158848 |
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| author | Affonso, Lucas Bissacot, Rodrigo Faria, Gilberto Welsch, Kelvyn |
| author_facet | Affonso, Lucas Bissacot, Rodrigo Faria, Gilberto Welsch, Kelvyn |
| contents | Using the group structure of the state space of $q-$state models, a new definition of contour for long-range spin-systems in $\Z^d$ ($d\geq 2$), and a multidimensional version of Fröhlich-Spencer contours, we prove phase transition for a class of ferromagnetic long-range systems which includes the Clock and Potts models. Our arguments work for the entire region of exponents of regular power-law interactions, namely $α> d$, and for any $q \geq 2$. As an application, we prove phase transition for Potts models with decaying fields when the field decays fast enough and in the presence of a random external field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_01234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase Transition in Long-Range $q-$state Models via Contours. Clock and Potts Models with Fields Affonso, Lucas Bissacot, Rodrigo Faria, Gilberto Welsch, Kelvyn Mathematical Physics Statistical Mechanics Probability 82Bxx, 82B20, 82B26 Using the group structure of the state space of $q-$state models, a new definition of contour for long-range spin-systems in $\Z^d$ ($d\geq 2$), and a multidimensional version of Fröhlich-Spencer contours, we prove phase transition for a class of ferromagnetic long-range systems which includes the Clock and Potts models. Our arguments work for the entire region of exponents of regular power-law interactions, namely $α> d$, and for any $q \geq 2$. As an application, we prove phase transition for Potts models with decaying fields when the field decays fast enough and in the presence of a random external field. |
| title | Phase Transition in Long-Range $q-$state Models via Contours. Clock and Potts Models with Fields |
| topic | Mathematical Physics Statistical Mechanics Probability 82Bxx, 82B20, 82B26 |
| url | https://arxiv.org/abs/2410.01234 |