Triple critical point and emerging temperature scales in $SU(N)$ ferromagnetism at large $N$
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| Format: | Preprint |
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2024
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| _version_ | 1866912445353689088 |
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| author | Polychronakos, Alexios P. Sfetsos, Konstantinos |
| author_facet | Polychronakos, Alexios P. Sfetsos, Konstantinos |
| contents | The non-Abelian ferromagnet recently introduced by the authors, consisting of atoms in the fundamental representation of $SU(N)$, is studied in the limit where $N$ becomes large and scales as the square root of the number of atoms $n$. This model exhibits additional phases, as well as two different temperature scales related by a factor $N\!/\!\ln N$. The paramagnetic phase splits into a "dense" and a "dilute" phase, separated by a third-order transition and leading to a triple critical point in the scale parameter $n/N^2$ and the temperature, while the ferromagnetic phase exhibits additional structure, and a new paramagnetic-ferromagnetic metastable phase appears at the larger temperature scale. These phases can coexist, becoming stable or metastable as temperature varies. A generalized model in which the number of $SU(N)$-equivalent states enters the partition function with a nontrivial weight, relevant, e.g., when there is gauge invariance in the system, is also studied and shown to manifest similar phases, with the dense-dilute phase transition becoming second-order in the fully gauge invariant case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triple critical point and emerging temperature scales in $SU(N)$ ferromagnetism at large $N$ Polychronakos, Alexios P. Sfetsos, Konstantinos High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems The non-Abelian ferromagnet recently introduced by the authors, consisting of atoms in the fundamental representation of $SU(N)$, is studied in the limit where $N$ becomes large and scales as the square root of the number of atoms $n$. This model exhibits additional phases, as well as two different temperature scales related by a factor $N\!/\!\ln N$. The paramagnetic phase splits into a "dense" and a "dilute" phase, separated by a third-order transition and leading to a triple critical point in the scale parameter $n/N^2$ and the temperature, while the ferromagnetic phase exhibits additional structure, and a new paramagnetic-ferromagnetic metastable phase appears at the larger temperature scale. These phases can coexist, becoming stable or metastable as temperature varies. A generalized model in which the number of $SU(N)$-equivalent states enters the partition function with a nontrivial weight, relevant, e.g., when there is gauge invariance in the system, is also studied and shown to manifest similar phases, with the dense-dilute phase transition becoming second-order in the fully gauge invariant case. |
| title | Triple critical point and emerging temperature scales in $SU(N)$ ferromagnetism at large $N$ |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2408.08357 |