Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins
Autor(a) principal: | |
---|---|
Data de Publicação: | 2012 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/8922 |
Resumo: | In this work, we present the results obtained for Ising models and Heisenberg spin 1/2, where two and three-dimensional, with disorder or frustration. We apply effective field theory associated with the Operator Differential Technique - TOD. A new formulation of this technique has enabled the development of a numerical implementation where the coefficients are now constructed fully automatically. This allowed growing up the number N of spins of the cluster and thus observe the behavior of the system when it tends to the real case (N→∞), which is bounded by the computational time needed to carry out all operations. We apply this methodology to study the Ising model with random field - RFIM, where we use three probability distributions for the field: bimodal, gaussian and gaussian double-peaked. The phase-diagrams were obtained in t - h plane for the cases Ferromagnetic-F and Antiferromagnetic-AF with the aid of Maxwell's construction procedure (equality of the free energies at line phase transition) identifying the tricritical point - PTC in each case. We present two proposals for obtaining the free energy, and in one of them it was possible to study the behavior of the thermodynamic properties in the regions of 1st and 2nd order. For a second application of numerical implementation, we use the quantum model of anisotropic Heisenberg spin (1/2) (with anisotropy parameter Δ), which lies in the particular cases that are important: one-dimensional Ising (Δ=1) and isotropic Heisenberg (Δ=0), being applied in the study of magnetic thin films formed by monolayers where the presence of free surfaces substantially alters the system behavior. We simulate this case, the spin frustration of considering interactions between the first (J₁) and second (J₂) interactions with neighboring F and AF respectively, being related by the parameter α=J₁/J₂. We studied the influence of increasing the dimensionality of the system, made by increasing the number of layers (L) of the film, the behavior of the phase diagram α - t. Finally, we apply the relations of the Renormalization Group in the Heisenberg Hamiltonian for a thin film to study the behavior of critical exponents as a function of parameters such as temperature and number of layers. |
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Amazonas, Márcio Andrei SousaSousa, José Ricardo dehttp://lattes.cnpq.br/3871066069541626Azevedo, José Roberto Vianahttp://lattes.cnpq.br/7115884585420145http://lattes.cnpq.br/0822367858729601ebe7b788-fa53-406d-a589-d7b78815c4a22017-08-07T18:31:02Z2017-08-07T18:31:02Z2012-10-11AMAZONAS, Márcio Andrei Sousa. Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins. 2012. Tese (Doutorado em Física) – Universidade Federal de São Carlos, São Carlos, 2012. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8922.https://repositorio.ufscar.br/handle/ufscar/8922In this work, we present the results obtained for Ising models and Heisenberg spin 1/2, where two and three-dimensional, with disorder or frustration. We apply effective field theory associated with the Operator Differential Technique - TOD. A new formulation of this technique has enabled the development of a numerical implementation where the coefficients are now constructed fully automatically. This allowed growing up the number N of spins of the cluster and thus observe the behavior of the system when it tends to the real case (N→∞), which is bounded by the computational time needed to carry out all operations. We apply this methodology to study the Ising model with random field - RFIM, where we use three probability distributions for the field: bimodal, gaussian and gaussian double-peaked. The phase-diagrams were obtained in t - h plane for the cases Ferromagnetic-F and Antiferromagnetic-AF with the aid of Maxwell's construction procedure (equality of the free energies at line phase transition) identifying the tricritical point - PTC in each case. We present two proposals for obtaining the free energy, and in one of them it was possible to study the behavior of the thermodynamic properties in the regions of 1st and 2nd order. For a second application of numerical implementation, we use the quantum model of anisotropic Heisenberg spin (1/2) (with anisotropy parameter Δ), which lies in the particular cases that are important: one-dimensional Ising (Δ=1) and isotropic Heisenberg (Δ=0), being applied in the study of magnetic thin films formed by monolayers where the presence of free surfaces substantially alters the system behavior. We simulate this case, the spin frustration of considering interactions between the first (J₁) and second (J₂) interactions with neighboring F and AF respectively, being related by the parameter α=J₁/J₂. We studied the influence of increasing the dimensionality of the system, made by increasing the number of layers (L) of the film, the behavior of the phase diagram α - t. Finally, we apply the relations of the Renormalization Group in the Heisenberg Hamiltonian for a thin film to study the behavior of critical exponents as a function of parameters such as temperature and number of layers.Apresentamos nesta tese os resultados obtidos para os modelos de Ising e Heisenberg de spin 1/2, nos casos bi e tridimensional, com desordem ou frustração. Aplicamos a teoria de campo efetivo associada à Técnica do Operador Diferencial - TOD. Uma nova formulação desta técnica permitiu o desenvolvimento de um algoritmo onde os coeficientes são agora construídos de forma totalmente automática. Isso possibilitou crescermos o número N de spins do aglomerado e assim observar o comportamento do sistema quando tende para o caso real (N→∞), tendo como limite o tempo computacional necessário para efetivar todas as operações. Aplicamos esta metodologia no estudo do modelo de Ising com campo aleatório - RFIM, onde utilizamos três distribuições de probabilidade para o campo: bimodal, gaussiana e gaussiana duplo-pico. Os diagramas de fase no plano t - h foram obtidos para os casos Ferromagnético-F e Antiferromagnético-AF com auxílio do procedimento da construção de Maxwell (igualdade das energias livres na linha de transição de fase), identificando o ponto tricrítico - PTC em cada caso. Apresentamos duas propostas para obtenção da energia livre, sendo que em uma delas foi possível o estudo do comportamento das propriedades termodinâmicas nas regiões de 1ª e 2ª ordem. Para uma segunda aplicação dessa implementação numérica, utilizamos o modelo de Heisenberg quântico de spin 1/2 anisotrópico (com parâmetro de anisotropia Δ), que recai nos casos particulares importantes que são: Ising unidimensional (Δ=1) e Heisenberg isotrópico (Δ=0), sendo aplicado no estudo de filmes finos magnéticos formados por monocamadas onde a presença de superfícies livres altera consideravelmente o comportamento do sistema. Simulamos nesse caso, a frustração dos spins considerando interações entre primeiros (J₁) e segundos (J₂) vizinhos com interações F e AF respectivamente, estando relacionados através do parâmetro α=J₁/J₂. Estudamos a influência do aumento da dimensionalidade do sistema, feito através do acréscimo no número de camadas (L) do filme, no comportamento do diagrama de fases t - α. Para finalizar, aplicamos as relações do Grupo de Renormalização no Hamiltoniano Heisenberg para um filme fino para o estudo do comportamento dos expoentes críticos em função de parâmetros como a temperatura e número de camadas.Fundação de Amparo à Pesquisa do Estado do Amazonas (FAPEAM)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Física - PPGFUFSCarTécnica do operador diferencialAlgoritmosModelo de IsingProbabilidadeCIENCIAS EXATAS E DA TERRA::FISICADesenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spinsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisOnline6006000c4db4d6-5aa4-4916-91f8-dbc89c346249info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTeseMASA.pdfTeseMASA.pdfapplication/pdf2952958https://repositorio.ufscar.br/bitstream/ufscar/8922/1/TeseMASA.pdf7fd6c19f5dbc2b559baf911ba11a9787MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/8922/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTTeseMASA.pdf.txtTeseMASA.pdf.txtExtracted texttext/plain285746https://repositorio.ufscar.br/bitstream/ufscar/8922/3/TeseMASA.pdf.txted62235e074da2861bbd43c1668654d9MD53THUMBNAILTeseMASA.pdf.jpgTeseMASA.pdf.jpgIM Thumbnailimage/jpeg8820https://repositorio.ufscar.br/bitstream/ufscar/8922/4/TeseMASA.pdf.jpgd9ef709dbc73b818aa740eaefdc7b754MD54ufscar/89222023-09-18 18:31:43.718oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:43Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins |
title |
Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins |
spellingShingle |
Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins Amazonas, Márcio Andrei Sousa Técnica do operador diferencial Algoritmos Modelo de Ising Probabilidade CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins |
title_full |
Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins |
title_fullStr |
Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins |
title_full_unstemmed |
Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins |
title_sort |
Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins |
author |
Amazonas, Márcio Andrei Sousa |
author_facet |
Amazonas, Márcio Andrei Sousa |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/0822367858729601 |
dc.contributor.author.fl_str_mv |
Amazonas, Márcio Andrei Sousa |
dc.contributor.advisor1.fl_str_mv |
Sousa, José Ricardo de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/3871066069541626 |
dc.contributor.advisor-co1.fl_str_mv |
Azevedo, José Roberto Viana |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/7115884585420145 |
dc.contributor.authorID.fl_str_mv |
ebe7b788-fa53-406d-a589-d7b78815c4a2 |
contributor_str_mv |
Sousa, José Ricardo de Azevedo, José Roberto Viana |
dc.subject.por.fl_str_mv |
Técnica do operador diferencial Algoritmos Modelo de Ising Probabilidade |
topic |
Técnica do operador diferencial Algoritmos Modelo de Ising Probabilidade CIENCIAS EXATAS E DA TERRA::FISICA |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::FISICA |
description |
In this work, we present the results obtained for Ising models and Heisenberg spin 1/2, where two and three-dimensional, with disorder or frustration. We apply effective field theory associated with the Operator Differential Technique - TOD. A new formulation of this technique has enabled the development of a numerical implementation where the coefficients are now constructed fully automatically. This allowed growing up the number N of spins of the cluster and thus observe the behavior of the system when it tends to the real case (N→∞), which is bounded by the computational time needed to carry out all operations. We apply this methodology to study the Ising model with random field - RFIM, where we use three probability distributions for the field: bimodal, gaussian and gaussian double-peaked. The phase-diagrams were obtained in t - h plane for the cases Ferromagnetic-F and Antiferromagnetic-AF with the aid of Maxwell's construction procedure (equality of the free energies at line phase transition) identifying the tricritical point - PTC in each case. We present two proposals for obtaining the free energy, and in one of them it was possible to study the behavior of the thermodynamic properties in the regions of 1st and 2nd order. For a second application of numerical implementation, we use the quantum model of anisotropic Heisenberg spin (1/2) (with anisotropy parameter Δ), which lies in the particular cases that are important: one-dimensional Ising (Δ=1) and isotropic Heisenberg (Δ=0), being applied in the study of magnetic thin films formed by monolayers where the presence of free surfaces substantially alters the system behavior. We simulate this case, the spin frustration of considering interactions between the first (J₁) and second (J₂) interactions with neighboring F and AF respectively, being related by the parameter α=J₁/J₂. We studied the influence of increasing the dimensionality of the system, made by increasing the number of layers (L) of the film, the behavior of the phase diagram α - t. Finally, we apply the relations of the Renormalization Group in the Heisenberg Hamiltonian for a thin film to study the behavior of critical exponents as a function of parameters such as temperature and number of layers. |
publishDate |
2012 |
dc.date.issued.fl_str_mv |
2012-10-11 |
dc.date.accessioned.fl_str_mv |
2017-08-07T18:31:02Z |
dc.date.available.fl_str_mv |
2017-08-07T18:31:02Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
AMAZONAS, Márcio Andrei Sousa. Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins. 2012. Tese (Doutorado em Física) – Universidade Federal de São Carlos, São Carlos, 2012. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8922. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/8922 |
identifier_str_mv |
AMAZONAS, Márcio Andrei Sousa. Desenvolvimento de um algoritmo numérico na técnica do operador diferencial : aplicações em modelos de spins. 2012. Tese (Doutorado em Física) – Universidade Federal de São Carlos, São Carlos, 2012. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8922. |
url |
https://repositorio.ufscar.br/handle/ufscar/8922 |
dc.language.iso.fl_str_mv |
por |
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por |
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600 600 |
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info:eu-repo/semantics/openAccess |
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openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Física - PPGF |
dc.publisher.initials.fl_str_mv |
UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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