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We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number n of fundamental representations of SU(N), and we identify a duality in the representation content of this decomposition. Our method utilizes the mapping of the representations of SU(N) to the states of free fermions on the circle, and can be viewed as a random walk on a multidimensional lattice. We also derive the large-n limit and the response of the system to an external non-abelian magnetic field. These results can be used to study the phase properties of non-abelian ferromagnets and to take various scaling limits.
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Ferromagnetic phase transitions in SU(N)
We study the thermodynamics of a non-abelian ferromagnet consisting of “atoms” each carrying a fun-damental representation of SU(N), coupled with long-range two-body quadratic interactions. We uncover a rich structure of phase transitions from non-magnetized, global SU(N)-invariant states to magnetized ones breaking global invariance to SU(N−1) ×U(1). Phases can coexist, one being stable and the other metastable, and the transition between states involves latent heat exchange, unlike in usual SU(2)ferro-magnets. Coupling the system to an external non-abelian magnetic field further enriches the phase structure, leading to additional phases. The system manifests hysteresis phenomena both in the magnetic field, as in usual ferromagnets, and in the temperature, in analogy to supercooled water. Potential applications are in fundamental situations or as a phenomenological model.
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- Award ID(s):
- 2112729
- PAR ID:
- 10532713
- Publisher / Repository:
- Nuclear Physics B
- Date Published:
- Journal Name:
- Nuclear Physics B
- Volume:
- 996
- Issue:
- C
- ISSN:
- 0550-3213
- Page Range / eLocation ID:
- 116353
- Subject(s) / Keyword(s):
- Ferromagnetism, nonabelian, SU(N), metastability, phase transitions, hysteresis
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.nuclphysb.2023.116353
