Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters
Ano de defesa: | 2020 |
---|---|
Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | , |
Tipo de documento: | Dissertação |
Tipo de acesso: | Acesso aberto |
Idioma: | por |
Instituição de defesa: |
Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas |
Programa de Pós-Graduação: |
Programa de Pós-Graduação em Física
|
Departamento: |
Física
|
País: |
Brasil
|
Palavras-chave em Português: | |
Palavras-chave em Inglês: | |
Área do conhecimento CNPq: | |
Link de acesso: | http://repositorio.ufsm.br/handle/1/21143 |
Resumo: | We study a model of localized spins which can assume three different states, S = 0 and 1, with two competing interactions: a antiferromagnetic first neighbour interaction (JA) and a three body interaction between third neighbours (JB), occurring only when there is a site in with S = 0 between the interacting states. We also consider a crystal field (D), which favors the states S = 0 when D < 0 and S = 1 when D > 0. We treated this model in a cluster mean-field approximation, which reduces a many-body problem to a effective single cluster one. In which, through Bogoliubov’s inequality, we use a variational principle to obtain an approximation to the free energy. Analyzing the behavior of the free energy and the order parameters, we can mark and characterize the phase transitions, allowing us to construct phase diagrams of the temperature by the third neighnour interaction and by the crystal field for different cluster sizes. From the analysis of the T=jJAj JB=jJAj phase diagram, we found that the competition between the first and third neighbor interaction is maximum at JB=jJAj = �����2, where the antiferromagnetic and super antiferromagnetic phases coexist at T = 0. Furthermore, our studies, through the analysis of the T=jJAj D=jJAj phase diagrams, demonstrate that incorporating clusters in the approach leads to a significant improvement in the obtained results when compared to the usual mean-field approach. Our cluster results also show the emergence of a new type of order in the system, called cluster antiferromagnetic, characterized by nonzero magnetizations in a square plaquette. In our analysis we shown that this order is a mixture of different microscopic states with non magnetic sites, which can difficult its characterization in Monte Carlo simulations. Another aspects in which the cluster approach improves the results is in the characterization of the phase transitions between the antiferromagnetic and paramagnetic phases. In particular, we hope that our investigation will motivate further studies of this model, considering different analytical and numerical methods |
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2021-06-17T18:24:01Z2021-06-17T18:24:01Z2020-04-27http://repositorio.ufsm.br/handle/1/21143We study a model of localized spins which can assume three different states, S = 0 and 1, with two competing interactions: a antiferromagnetic first neighbour interaction (JA) and a three body interaction between third neighbours (JB), occurring only when there is a site in with S = 0 between the interacting states. We also consider a crystal field (D), which favors the states S = 0 when D < 0 and S = 1 when D > 0. We treated this model in a cluster mean-field approximation, which reduces a many-body problem to a effective single cluster one. In which, through Bogoliubov’s inequality, we use a variational principle to obtain an approximation to the free energy. Analyzing the behavior of the free energy and the order parameters, we can mark and characterize the phase transitions, allowing us to construct phase diagrams of the temperature by the third neighnour interaction and by the crystal field for different cluster sizes. From the analysis of the T=jJAj JB=jJAj phase diagram, we found that the competition between the first and third neighbor interaction is maximum at JB=jJAj = �����2, where the antiferromagnetic and super antiferromagnetic phases coexist at T = 0. Furthermore, our studies, through the analysis of the T=jJAj D=jJAj phase diagrams, demonstrate that incorporating clusters in the approach leads to a significant improvement in the obtained results when compared to the usual mean-field approach. Our cluster results also show the emergence of a new type of order in the system, called cluster antiferromagnetic, characterized by nonzero magnetizations in a square plaquette. In our analysis we shown that this order is a mixture of different microscopic states with non magnetic sites, which can difficult its characterization in Monte Carlo simulations. Another aspects in which the cluster approach improves the results is in the characterization of the phase transitions between the antiferromagnetic and paramagnetic phases. In particular, we hope that our investigation will motivate further studies of this model, considering different analytical and numerical methodsEstudamos um modelo de spins localizados, os quais podem assumir três estados distintos, S = 0 e 1, com duas interações competitivas: uma interação antiferromagnética entre primeiros vizinhos (JA) e uma interação de três corpos entre terceiros vizinhos (JB), a qual ocorre apenas quando existe um sítio com spin nulo (S = 0) entre sítios interagentes. Consideramos também um campo de cristal (D), o qual favorece os estados S = 0 quando D < 0 e S = 1 quando D > 0. Tratamos este modelo através de uma aproximação de campo médio com clusters, a qual reduz o problema de muitos corpos a um problema efetivo de um único cluster. Neste, através da desigualdade de Bogoliubov, utilizamos um princípio variacional para obter uma energia livre aproximada. Analisando o comportamento da energia livre e dos parâmetros de ordem, marcamos e caracterizamos as transições de fase do sistema, construindo diagramas de fase da temperatura T pela interação de terceiros vizinhos e da temperatura pelo campo de cristal para diferentes tamanhos de cluster. A partir da análise do diagrama de fases para T=jJAj JB=jJAj, verificamos que a competição entre as interações consideradas é máxima em JB=jJAj = 2, onde as fases antiferromagnética e super antiferromagnética coexistem em T = 0. Além disso, a análise dos diagramas T=jJAj D=jJAj, demonstram que incorporar clusters na aproximação de campo médio leva a uma significativa melhora nos resultados em relação à aproximação de campo médio canônica. Nossos resultados com clusters sugerem o surgimento de um novo tipo de ordenamento, denominado cluster antiferromagnético, o qual é caracterizado por sítios com magnetizações não nulas dentro de plaquetas quadradas. Em nossa análise demonstramos que este ordenamento é uma mistura de diferentes estados microscópicos com alguns sítios não magnéticos, o que pode dificultar sua caracterização em uma simulação de Monte Carlo. Outro aspecto em que a aproximação com clusters melhora os resultados é na caracterização das transições da fase antiferromagnética para a paramagnética Em particular, esperamos que nossa investigação motive outros estudos deste modelo, considerando diferentes métodos analíticos e numéricos.porUniversidade Federal de Santa MariaCentro de Ciências Naturais e ExatasPrograma de Pós-Graduação em FísicaUFSMBrasilFísicaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessInterações competitivasTeoria de campo médio com clustersTransições de faseCompeting interactionsCluster mean-field theoryPhase transitionsCNPQ::CIENCIAS EXATAS E DA TERRA::FISICASistemas magnéticos com interações competitivas: uma abordagem de campo médio com clustersinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisZimmer, Fábio Mallmannhttp://lattes.cnpq.br/6328420212181284Schmidt, MateusXXXXXXXXXXXXXXCalegari, Eleonir JoãoXXXXXXXXXXXXXXXMetz, Fernando LucasXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXFrantz, Gustavo Luis Kohlrausch100500000006600e33a6993-09ff-40de-b1e8-1a3a0fd077d2091516ad-a3dc-4826-a23a-f1c4bc5217bbd8fc0c2e-572c-4264-8c9d-7b25734b62bcb1b7fd5e-74b1-4c31-a40c-bf85e3530c8fceb7c335-c037-4236-8ee9-ea79b2439cc2reponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.por.fl_str_mv |
Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters |
title |
Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters |
spellingShingle |
Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters Frantz, Gustavo Luis Kohlrausch Interações competitivas Teoria de campo médio com clusters Transições de fase Competing interactions Cluster mean-field theory Phase transitions CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters |
title_full |
Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters |
title_fullStr |
Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters |
title_full_unstemmed |
Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters |
title_sort |
Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters |
author |
Frantz, Gustavo Luis Kohlrausch |
author_facet |
Frantz, Gustavo Luis Kohlrausch |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Zimmer, Fábio Mallmann |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/6328420212181284 |
dc.contributor.advisor-co1.fl_str_mv |
Schmidt, Mateus |
dc.contributor.advisor-co1Lattes.fl_str_mv |
XXXXXXXXXXXXXX |
dc.contributor.referee1.fl_str_mv |
Calegari, Eleonir João |
dc.contributor.referee1Lattes.fl_str_mv |
XXXXXXXXXXXXXXX |
dc.contributor.referee2.fl_str_mv |
Metz, Fernando Lucas |
dc.contributor.referee2Lattes.fl_str_mv |
XXXXXXXXXXXXXX |
dc.contributor.authorLattes.fl_str_mv |
XXXXXXXXXXXXXXXXXXXXXX |
dc.contributor.author.fl_str_mv |
Frantz, Gustavo Luis Kohlrausch |
contributor_str_mv |
Zimmer, Fábio Mallmann Schmidt, Mateus Calegari, Eleonir João Metz, Fernando Lucas |
dc.subject.por.fl_str_mv |
Interações competitivas Teoria de campo médio com clusters Transições de fase |
topic |
Interações competitivas Teoria de campo médio com clusters Transições de fase Competing interactions Cluster mean-field theory Phase transitions CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
dc.subject.eng.fl_str_mv |
Competing interactions Cluster mean-field theory Phase transitions |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
description |
We study a model of localized spins which can assume three different states, S = 0 and 1, with two competing interactions: a antiferromagnetic first neighbour interaction (JA) and a three body interaction between third neighbours (JB), occurring only when there is a site in with S = 0 between the interacting states. We also consider a crystal field (D), which favors the states S = 0 when D < 0 and S = 1 when D > 0. We treated this model in a cluster mean-field approximation, which reduces a many-body problem to a effective single cluster one. In which, through Bogoliubov’s inequality, we use a variational principle to obtain an approximation to the free energy. Analyzing the behavior of the free energy and the order parameters, we can mark and characterize the phase transitions, allowing us to construct phase diagrams of the temperature by the third neighnour interaction and by the crystal field for different cluster sizes. From the analysis of the T=jJAj JB=jJAj phase diagram, we found that the competition between the first and third neighbor interaction is maximum at JB=jJAj = �����2, where the antiferromagnetic and super antiferromagnetic phases coexist at T = 0. Furthermore, our studies, through the analysis of the T=jJAj D=jJAj phase diagrams, demonstrate that incorporating clusters in the approach leads to a significant improvement in the obtained results when compared to the usual mean-field approach. Our cluster results also show the emergence of a new type of order in the system, called cluster antiferromagnetic, characterized by nonzero magnetizations in a square plaquette. In our analysis we shown that this order is a mixture of different microscopic states with non magnetic sites, which can difficult its characterization in Monte Carlo simulations. Another aspects in which the cluster approach improves the results is in the characterization of the phase transitions between the antiferromagnetic and paramagnetic phases. In particular, we hope that our investigation will motivate further studies of this model, considering different analytical and numerical methods |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020-04-27 |
dc.date.accessioned.fl_str_mv |
2021-06-17T18:24:01Z |
dc.date.available.fl_str_mv |
2021-06-17T18:24:01Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
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masterThesis |
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publishedVersion |
dc.identifier.uri.fl_str_mv |
http://repositorio.ufsm.br/handle/1/21143 |
url |
http://repositorio.ufsm.br/handle/1/21143 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.cnpq.fl_str_mv |
100500000006 |
dc.relation.confidence.fl_str_mv |
600 |
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dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Física |
dc.publisher.initials.fl_str_mv |
UFSM |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Física |
publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
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