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We present a general formalism for deriving the thermodynamics of ferromagnets consisting of "atoms" carrying an arbitrary irreducible representation of and coupled through long-range two-body quadratic interactions. Using this formalism, we derive the thermodynamics and phase structure of ferromagnets with atoms in the doubly symmetric or doubly antisymmetric irreducible representations. The symmetric representation leads to a paramagnetic and a ferromagnetic phase with transitions similar to the ones for the fundamental representation studied before. The antisymmetric representation presents qualitatively new features, leading to a paramagnetic and two distinct ferromagnetic phases that can coexist over a range of temperatures, two of them becoming metastable. Our results are relevant to magnetic systems of atoms with reduced symmetry in their interactions compared to the fundamental case.
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Triple critical point and emerging temperature scales in SU(N) ferromagnetism at large N
The non-Abelian ferromagnet recently introduced by the authors, consisting of atoms in the fundamental representation of , is studied in the limit where becomes large and scales as the square root of the number of atoms . This model exhibits additional phases, as well as two different temperature scales related by a factor . 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 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 -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.
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- Award ID(s):
- 2412479
- PAR ID:
- 10599415
- Publisher / Repository:
- Nuclear Physics B
- Date Published:
- Journal Name:
- Nuclear Physics B
- Volume:
- 1009
- Issue:
- C
- ISSN:
- 0550-3213
- Page Range / eLocation ID:
- 116748
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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