Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice

Autores
Honecker, Andreas; Cabra, Daniel Carlos; Everts, H.-U.; Pujol, Pierre; Stauffer, Franck
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Frustration has proven to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model in which only the lowest-energy degrees of freedom are considered. In this paper, we study a system corresponding to the strong trimerization limit of the spin-1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin-1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J > 0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J > 0 and J < 0, a finite-temperature phase transition with a breaking of the discrete dihedral symmetry group D6 of the model is present. For J < 0, we find a transition temperature T < c /|J | = 1.566 ± 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J > 0, the transition occurs at an extremely low temperature, T > c ≈ 0.0125 J . Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case.
Instituto de Física La Plata
Materia
Física
Physics
Phase transition
Antiferromagnetism
Critical exponent
Coupling constant
Condensed matter physics
Spin model
Frustration
Classical limit
Quantum mechanics
Hexagonal lattice
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/126457

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network_name_str SEDICI (UNLP)
spelling Order by disorder and phase transitions in a highly frustrated spin model on the triangular latticeHonecker, AndreasCabra, Daniel CarlosEverts, H.-U.Pujol, PierreStauffer, FranckFísicaPhysicsPhase transitionAntiferromagnetismCritical exponentCoupling constantCondensed matter physicsSpin modelFrustrationClassical limitQuantum mechanicsHexagonal latticeFrustration has proven to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model in which only the lowest-energy degrees of freedom are considered. In this paper, we study a system corresponding to the strong trimerization limit of the spin-1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin-1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J &gt; 0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J &gt; 0 and J &lt; 0, a finite-temperature phase transition with a breaking of the discrete dihedral symmetry group D6 of the model is present. For J &lt; 0, we find a transition temperature T &lt; c /|J | = 1.566 ± 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J &gt; 0, the transition occurs at an extremely low temperature, T &gt; c ≈ 0.0125 J . Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case.Instituto de Física La Plata2011-12-14info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/126457enginfo:eu-repo/semantics/altIdentifier/issn/1098-0121info:eu-repo/semantics/altIdentifier/issn/1550-235xinfo:eu-repo/semantics/altIdentifier/arxiv/1108.5268info:eu-repo/semantics/altIdentifier/doi/10.1103/physrevb.84.224410info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:30:23Zoai:sedici.unlp.edu.ar:10915/126457Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:30:24.114SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
title Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
spellingShingle Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
Honecker, Andreas
Física
Physics
Phase transition
Antiferromagnetism
Critical exponent
Coupling constant
Condensed matter physics
Spin model
Frustration
Classical limit
Quantum mechanics
Hexagonal lattice
title_short Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
title_full Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
title_fullStr Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
title_full_unstemmed Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
title_sort Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
dc.creator.none.fl_str_mv Honecker, Andreas
Cabra, Daniel Carlos
Everts, H.-U.
Pujol, Pierre
Stauffer, Franck
author Honecker, Andreas
author_facet Honecker, Andreas
Cabra, Daniel Carlos
Everts, H.-U.
Pujol, Pierre
Stauffer, Franck
author_role author
author2 Cabra, Daniel Carlos
Everts, H.-U.
Pujol, Pierre
Stauffer, Franck
author2_role author
author
author
author
dc.subject.none.fl_str_mv Física
Physics
Phase transition
Antiferromagnetism
Critical exponent
Coupling constant
Condensed matter physics
Spin model
Frustration
Classical limit
Quantum mechanics
Hexagonal lattice
topic Física
Physics
Phase transition
Antiferromagnetism
Critical exponent
Coupling constant
Condensed matter physics
Spin model
Frustration
Classical limit
Quantum mechanics
Hexagonal lattice
dc.description.none.fl_txt_mv Frustration has proven to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model in which only the lowest-energy degrees of freedom are considered. In this paper, we study a system corresponding to the strong trimerization limit of the spin-1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin-1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J &gt; 0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J &gt; 0 and J &lt; 0, a finite-temperature phase transition with a breaking of the discrete dihedral symmetry group D6 of the model is present. For J &lt; 0, we find a transition temperature T &lt; c /|J | = 1.566 ± 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J &gt; 0, the transition occurs at an extremely low temperature, T &gt; c ≈ 0.0125 J . Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case.
Instituto de Física La Plata
description Frustration has proven to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model in which only the lowest-energy degrees of freedom are considered. In this paper, we study a system corresponding to the strong trimerization limit of the spin-1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin-1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J &gt; 0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J &gt; 0 and J &lt; 0, a finite-temperature phase transition with a breaking of the discrete dihedral symmetry group D6 of the model is present. For J &lt; 0, we find a transition temperature T &lt; c /|J | = 1.566 ± 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J &gt; 0, the transition occurs at an extremely low temperature, T &gt; c ≈ 0.0125 J . Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case.
publishDate 2011
dc.date.none.fl_str_mv 2011-12-14
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/126457
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dc.language.none.fl_str_mv eng
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info:eu-repo/semantics/altIdentifier/issn/1550-235x
info:eu-repo/semantics/altIdentifier/arxiv/1108.5268
info:eu-repo/semantics/altIdentifier/doi/10.1103/physrevb.84.224410
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
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Creative Commons Attribution 4.0 International (CC BY 4.0)
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