Simulações entrópicas do Modelo de Baxter-Wu
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/7777 |
Resumo: | In this work, we used a refined entropy sampling technique based on the Wang- Landau method and finite-size scaling techniques to study variations of the Baxter-Wu model, namely: spin-$1/2$, spin-$1$, spin-$1$ with the crystal field interaction and was done a three-dimensional proposal for the model. It was also verified characteristics in the order parameter to be adopted in the simulations. The universality class and the critical temperature were calculated for the spin-$1/2$ case, and the results founded were in good agreement with the exact ones found in the literature. We sought to determine the kind of the phase transition that the model suffers for the spin-$1$ case, being carried out a detailed study for continuous and discontinuous phase transitions. The Baxter-Wu model with crystal field, $D$, had its phase diagram constructed, as well as the determination of the point at which discontinuous transitions finalizes. The critical exponent, $\nu$, was evaluated for several values of the crystal field, where we verified is variation along the critical line, with the existence of a peak, corroborating the existence of a multicritic behavior of the model. We also observed the existence of an anomaly in the specific heat, associated to the Schottky defect. This anomaly appears more clearly for values of $D \geq 1.990$. In the study of the order parameter, we verified that in the simulations one should not, when considering lattice sizes multiple of three, use the order parameter as the total magnetization of the lattice, but to consider the magnetization by sub-lattices. When working with sizes of lattices that are not multiples of three, it is not a problem to adopt the order parameter as the total magnetization of the lattice. A three-dimensional proposal was also made for the Baxter-Wu model, and its phase transition was characterized. |
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Caparica, Álvaro de Almeidahttp://lattes.cnpq.br/4726638254587108Sousa, José Ricardo deGodoy, MaurícioVale, Renato PessoaSilva, Hermann Freire Ferreira Lima ehttp://lattes.cnpq.br/4897480282945507Jorge, Lucas Nunes2017-09-21T10:49:25Z2017-08-04JORGE, L. N. Simulações entrópicas do Modelo de Baxter-Wu. 2017. 107 f. Tese (Doutorado em Física) - Universidade Federal de Goiás, Goiânia, 2017.http://repositorio.bc.ufg.br/tede/handle/tede/7777ark:/38995/0013000000hjrIn this work, we used a refined entropy sampling technique based on the Wang- Landau method and finite-size scaling techniques to study variations of the Baxter-Wu model, namely: spin-$1/2$, spin-$1$, spin-$1$ with the crystal field interaction and was done a three-dimensional proposal for the model. It was also verified characteristics in the order parameter to be adopted in the simulations. The universality class and the critical temperature were calculated for the spin-$1/2$ case, and the results founded were in good agreement with the exact ones found in the literature. We sought to determine the kind of the phase transition that the model suffers for the spin-$1$ case, being carried out a detailed study for continuous and discontinuous phase transitions. The Baxter-Wu model with crystal field, $D$, had its phase diagram constructed, as well as the determination of the point at which discontinuous transitions finalizes. The critical exponent, $\nu$, was evaluated for several values of the crystal field, where we verified is variation along the critical line, with the existence of a peak, corroborating the existence of a multicritic behavior of the model. We also observed the existence of an anomaly in the specific heat, associated to the Schottky defect. This anomaly appears more clearly for values of $D \geq 1.990$. In the study of the order parameter, we verified that in the simulations one should not, when considering lattice sizes multiple of three, use the order parameter as the total magnetization of the lattice, but to consider the magnetization by sub-lattices. When working with sizes of lattices that are not multiples of three, it is not a problem to adopt the order parameter as the total magnetization of the lattice. A three-dimensional proposal was also made for the Baxter-Wu model, and its phase transition was characterized.Neste trabalho, utilizamos uma técnica de amostragem entrópica com refinamentos baseada no método de Wang-Landau e técnicas de escala de tamanho finito para estudar variações do modelo de Baxter-Wu, a saber: spin-$1/2$, spin-$1$, spin-$1$ na presença de anisotropia de campo cristalino, onde também foi feita uma proposta tridimensional para o modelo. Foram verificadas também características no parâmetro de ordem a ser adotado nas simulações. A classe de universalidade e a temperatura crítica foram calculadas para o caso spin-$1/2$, e os resultados encontrados tiveram boa concordância com os resultados exatos que constam na literatura. Buscou-se determinar o tipo de transição de fase que o modelo descreve para o caso spin-$1$, sendo feito um detalhado estudo para transições de fases contínua e descontínua. O modelo de Baxter-Wu com interação do campo cristalino, $D$, teve o seu diagrama de fases construído, bem como a determinação do ponto em que terminam as transições descontínuas. O expoente crítico, $\nu$, foi avaliado para diversos valores do campo cristalino, onde verificamos a sua variação ao longo da linha crítica, com o aparecimento de um pico, corroborando a existência de um comportamento multicrítico do modelo. Observamos também uma anomalia no calor específico, que pode ser associada ao defeito Schottky. Essa anomalia aparece de maneira mais significativa para valores de $D\geqslant1.990$. No estudo do parâmetro de ordem, verificamos que nas simulações não se deve, ao considerar tamanhos de redes múltiplos de três, utilizar o parâmetro de ordem como a magnetização total da rede, mas tomar a magnetização por sub-redes. Ao se trabalhar com tamanhos de redes que não sejam múltiplos de três, não há problema em adotá-lo como a magnetização total da rede. Foi feita também uma proposta tridimensional para o modelo de Baxter-Wu, e foi caracterizada a sua transição de fases.Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-09-20T19:09:51Z No. of bitstreams: 2 Tese - Lucas Nunes Jorge - 2017.pdf: 5873752 bytes, checksum: 804e244800839331e5594855dcd427a8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-09-21T10:49:25Z (GMT) No. of bitstreams: 2 Tese - Lucas Nunes Jorge - 2017.pdf: 5873752 bytes, checksum: 804e244800839331e5594855dcd427a8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2017-09-21T10:49:25Z (GMT). No. of bitstreams: 2 Tese - Lucas Nunes Jorge - 2017.pdf: 5873752 bytes, checksum: 804e244800839331e5594855dcd427a8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-08-04Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEGapplication/pdfporUniversidade Federal de GoiásPrograma de Pós-graduação em Fisica (IF)UFGBrasilInstituto de Física - IF (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAmostragem entrópicaModelo de Baxter-WuClasse de universalidadeTemperatura críticaEntropic samplingBaxter-Wu ModelUniversality classCritical temperatureFISICA GERAL::FISICA ESTATISTICA E TERMODINAMICASimulações entrópicas do Modelo de Baxter-WuEntropic simulations of the Baxter-Wu Modelinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis3162138865744262028600600600600-4029658853652049306-2015905348453256065-961409807440757778reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.eng.fl_str_mv |
Simulações entrópicas do Modelo de Baxter-Wu |
dc.title.alternative.eng.fl_str_mv |
Entropic simulations of the Baxter-Wu Model |
title |
Simulações entrópicas do Modelo de Baxter-Wu |
spellingShingle |
Simulações entrópicas do Modelo de Baxter-Wu Jorge, Lucas Nunes Amostragem entrópica Modelo de Baxter-Wu Classe de universalidade Temperatura crítica Entropic sampling Baxter-Wu Model Universality class Critical temperature FISICA GERAL::FISICA ESTATISTICA E TERMODINAMICA |
title_short |
Simulações entrópicas do Modelo de Baxter-Wu |
title_full |
Simulações entrópicas do Modelo de Baxter-Wu |
title_fullStr |
Simulações entrópicas do Modelo de Baxter-Wu |
title_full_unstemmed |
Simulações entrópicas do Modelo de Baxter-Wu |
title_sort |
Simulações entrópicas do Modelo de Baxter-Wu |
author |
Jorge, Lucas Nunes |
author_facet |
Jorge, Lucas Nunes |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Caparica, Álvaro de Almeida |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/4726638254587108 |
dc.contributor.referee1.fl_str_mv |
Sousa, José Ricardo de |
dc.contributor.referee2.fl_str_mv |
Godoy, Maurício |
dc.contributor.referee3.fl_str_mv |
Vale, Renato Pessoa |
dc.contributor.referee4.fl_str_mv |
Silva, Hermann Freire Ferreira Lima e |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/4897480282945507 |
dc.contributor.author.fl_str_mv |
Jorge, Lucas Nunes |
contributor_str_mv |
Caparica, Álvaro de Almeida Sousa, José Ricardo de Godoy, Maurício Vale, Renato Pessoa Silva, Hermann Freire Ferreira Lima e |
dc.subject.por.fl_str_mv |
Amostragem entrópica Modelo de Baxter-Wu Classe de universalidade Temperatura crítica |
topic |
Amostragem entrópica Modelo de Baxter-Wu Classe de universalidade Temperatura crítica Entropic sampling Baxter-Wu Model Universality class Critical temperature FISICA GERAL::FISICA ESTATISTICA E TERMODINAMICA |
dc.subject.eng.fl_str_mv |
Entropic sampling Baxter-Wu Model Universality class Critical temperature |
dc.subject.cnpq.fl_str_mv |
FISICA GERAL::FISICA ESTATISTICA E TERMODINAMICA |
description |
In this work, we used a refined entropy sampling technique based on the Wang- Landau method and finite-size scaling techniques to study variations of the Baxter-Wu model, namely: spin-$1/2$, spin-$1$, spin-$1$ with the crystal field interaction and was done a three-dimensional proposal for the model. It was also verified characteristics in the order parameter to be adopted in the simulations. The universality class and the critical temperature were calculated for the spin-$1/2$ case, and the results founded were in good agreement with the exact ones found in the literature. We sought to determine the kind of the phase transition that the model suffers for the spin-$1$ case, being carried out a detailed study for continuous and discontinuous phase transitions. The Baxter-Wu model with crystal field, $D$, had its phase diagram constructed, as well as the determination of the point at which discontinuous transitions finalizes. The critical exponent, $\nu$, was evaluated for several values of the crystal field, where we verified is variation along the critical line, with the existence of a peak, corroborating the existence of a multicritic behavior of the model. We also observed the existence of an anomaly in the specific heat, associated to the Schottky defect. This anomaly appears more clearly for values of $D \geq 1.990$. In the study of the order parameter, we verified that in the simulations one should not, when considering lattice sizes multiple of three, use the order parameter as the total magnetization of the lattice, but to consider the magnetization by sub-lattices. When working with sizes of lattices that are not multiples of three, it is not a problem to adopt the order parameter as the total magnetization of the lattice. A three-dimensional proposal was also made for the Baxter-Wu model, and its phase transition was characterized. |
publishDate |
2017 |
dc.date.accessioned.fl_str_mv |
2017-09-21T10:49:25Z |
dc.date.issued.fl_str_mv |
2017-08-04 |
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 |
JORGE, L. N. Simulações entrópicas do Modelo de Baxter-Wu. 2017. 107 f. Tese (Doutorado em Física) - Universidade Federal de Goiás, Goiânia, 2017. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/7777 |
dc.identifier.dark.fl_str_mv |
ark:/38995/0013000000hjr |
identifier_str_mv |
JORGE, L. N. Simulações entrópicas do Modelo de Baxter-Wu. 2017. 107 f. Tese (Doutorado em Física) - Universidade Federal de Goiás, Goiânia, 2017. ark:/38995/0013000000hjr |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/7777 |
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por |
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por |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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UFG |
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Brasil |
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Instituto de Física - IF (RG) |
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Universidade Federal de Goiás |
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