Classical SO(n) spins on geometrically frustrated crystals: A real-space renormalization group spproach
A real-space renormalization group (RG) framework is formulated for classical SO(n) spin models defined on d-dimensional crystal lattices composed of corner-sharing hyper-tetrahedra, a class of geometrically frustrated crystal structures. This includes, as specific instances, the classical Heisenber...
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| Tipo de documento: | artigo |
| Data de publicação: | 2025 |
| País: | España |
| Recursos: | Universidad del País Vasco |
| Repositório: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/77135 |
| Acesso em linha: | http://hdl.handle.net/10810/77135 |
| Access Level: | Acceso aberto |
| Palavra-chave: | classical vector spins n-vector models geometrical frustration pyrochlore lattice kagome lattice |
| Resumo: | A real-space renormalization group (RG) framework is formulated for classical SO(n) spin models defined on d-dimensional crystal lattices composed of corner-sharing hyper-tetrahedra, a class of geometrically frustrated crystal structures. This includes, as specific instances, the classical Heisenberg model on the kagome and pyrochlore crystals. The approach involves computing the partition function and corresponding order parameters for spin clusters embedded in the crystal, to leading order in symmetry-breaking fields generated by surrounding spins. The crystal geometry plays a central role in determining the scaling relations and the associated critical behavior. To illustrate the efficacy of the method, a reduced manifold of symmetry-allowed ordered states for isotropic nearest-neighbor interactions is analyzed. The RG flow systematically excludes the emergence of a q ->=0 ordered phase within the antiferromagnetic sector, independently of both the spatial dimensionality of the crystal and the number of spin components. Extensions to incorporate more elaborate crystal-symmetry-induced ordering patterns and fluctuation-driven phenomena-such as order-by-disorder-are also discussed. |
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