Criticalidade do modelo de Ising tridimensional : um estudo dinâmico
Autor(a) principal: | |
---|---|
Data de Publicação: | 2015 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UFRPE |
Texto Completo: | http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8510 |
Resumo: | In this work we investigate the criticality of the three-dimensional Ising model with interactions between rst neighbors. In our computational simulations we consider that the spins are distributed in a simple cubic lattice of side L, and lattice parameter a, so the number of spins in the lattice is N = (L=a)3. We employ periodical conditions of contour to describe the volumetric limit, in which the border and nite-size e ects are eliminated. We investigate the critical behavior of the system through the dynamic relaxation technique in short terms where the system evolves according to the Metropolis dynamic. Futhermore, the system properties are calculated before it reaches a state of equilibrium. Here, we consider only evolution from a completely ordered state, that is, the magnetization density of the system at the initial time is unitary. We calculate the magnetization (M), the structure factor (Sk), the time-dependent correlation length ( ), the uctuation of the order parameter (4m) and the second cumulante of Binder (U2). The value of the inverse of the critical temperature, Kc, was estimated using a method that explores the scale behavior of the derivative logarithm of the order parameter with respect to the logarithm of time (t; "), where " measures the distance to the critical point. The quantity (t; ") gives, besides the value of Kc, estimates for the critical exponents , and . The technique of data collapse is used for the purpose of obtaining greater accuracy in the values of the critical parameters obtained. The results found in this work for the critical parameter Kc = 0; 22166(3) and for the critical exponents = 0; 6495(3), = 1,2884(5) and = 0; 3222(3), were compared with others available in the recent specialized literature, for systems that are in the same class as the universality of the three-dimensional Ising model, in which we nd concordance until the fth decimal place through a technique that has a low computational requirement. |
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SOUZA, Adauto José Ferreira deROMAGUERA, Antônio Rodrigues de CastroVILELA, André Luis da Motahttp://lattes.cnpq.br/0227684644192779SANTOS, Jorge Gustavo Bandeira dos2020-10-13T21:25:03Z2015-08-13SANTOS, Jorge Gustavo Bandeira dos. Criticalidade do modelo de Ising tridimensional : um estudo dinâmico. 2015. 59 f. Dissertação (Programa de Pós-Graduação em Física Aplicada) - Universidade Federal Rural de Pernambuco, Recife.http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8510In this work we investigate the criticality of the three-dimensional Ising model with interactions between rst neighbors. In our computational simulations we consider that the spins are distributed in a simple cubic lattice of side L, and lattice parameter a, so the number of spins in the lattice is N = (L=a)3. We employ periodical conditions of contour to describe the volumetric limit, in which the border and nite-size e ects are eliminated. We investigate the critical behavior of the system through the dynamic relaxation technique in short terms where the system evolves according to the Metropolis dynamic. Futhermore, the system properties are calculated before it reaches a state of equilibrium. Here, we consider only evolution from a completely ordered state, that is, the magnetization density of the system at the initial time is unitary. We calculate the magnetization (M), the structure factor (Sk), the time-dependent correlation length ( ), the uctuation of the order parameter (4m) and the second cumulante of Binder (U2). The value of the inverse of the critical temperature, Kc, was estimated using a method that explores the scale behavior of the derivative logarithm of the order parameter with respect to the logarithm of time (t; "), where " measures the distance to the critical point. The quantity (t; ") gives, besides the value of Kc, estimates for the critical exponents , and . The technique of data collapse is used for the purpose of obtaining greater accuracy in the values of the critical parameters obtained. The results found in this work for the critical parameter Kc = 0; 22166(3) and for the critical exponents = 0; 6495(3), = 1,2884(5) and = 0; 3222(3), were compared with others available in the recent specialized literature, for systems that are in the same class as the universality of the three-dimensional Ising model, in which we nd concordance until the fth decimal place through a technique that has a low computational requirement.Neste trabalho investigamos a criticalidade do modelo de Ising tridimensional com interações entre primeiros vizinhos. Em nossas simulações computacionais consideramos que os spins estão distribuídos numa rede cúbica simples de lado L e parâmetro de rede a, de maneira que o número de spins na rede é N = (L=a)3. Empregamos condições de contorno periódicas para descrever o limite volumétrico, na qual os efeitos de fronteira e de tamanho nito são eliminados. Investigamos o comportamento crítico do sistema através da técnica de relaxação dinâmica em tempos curtos onde o sistema evolui segundo a dinâmica de Metropolis. Além disso, as propriedades do sistema são calculadas antes que o mesmo atinja um estado de equilíbrio. Aqui, consideramos apenas a evolução a partir de um estado completamente ordenado, ou seja, a densidade de magnetização do sistema no instante inicial é unitária. Calculamos a magnetização (M), o fator de estrutura (Sk), o comprimento de correlação dependente do tempo ( ), a utuação do parâmetro de ordem ( m) e o segundo cumulante de Binder (U2). O valor do inverso da temperatura crítica, Kc, foi estimado utilizando um método que explora o comportamento de escala da derivada do logaritmo do parâmetro de ordem com respeito ao logaritmo do tempo (t; "), onde " mede a distância ao ponto crítico. A grandeza (t; ") fornece, além do valor de Kc, estimativas para os expoentes críticos , e . A técnica de colapso de dados é utilizada com o propósito de se obter uma maior precisão nos valores dos parâmetros críticos obtidos. Os resultados encontrados neste trabalho para o parâmerto crítico Kc = 0; 22166(3) e para os expoentes críticos = 0; 6495(3), = 1; 2884(5) e = 0; 3222(3), foram comparados com outros disponíveis na literatura especializada recente, para sistemas que estão na mesma classe de universalidade que o modelo de Ising tridimensional, no qual encontramos concordância até a quinta casa decimal através de uma técnica que possui baixa exigência computacional.Submitted by Mario BC (mario@bc.ufrpe.br) on 2020-10-13T21:25:03Z No. of bitstreams: 1 Jorge Gustavo Bandeira dos Santos.pdf: 964319 bytes, checksum: 6bbe56bd95fb1eb09406170addbbb499 (MD5)Made available in DSpace on 2020-10-13T21:25:03Z (GMT). No. of bitstreams: 1 Jorge Gustavo Bandeira dos Santos.pdf: 964319 bytes, checksum: 6bbe56bd95fb1eb09406170addbbb499 (MD5) Previous issue date: 2015-08-13Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade Federal Rural de PernambucoPrograma de Pós-Graduação em Física AplicadaUFRPEBrasilDepartamento de FísicaModelo de IsingDinâmica de MetropolisMagnetizaçãoCIENCIAS EXATAS E DA TERRA::FISICACriticalidade do modelo de Ising tridimensional : um estudo dinâmicoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis2948194971945047520600600600600-748177341945315287-83271462965037459292075167498588264571info:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFRPEinstname:Universidade Federal Rural de Pernambuco (UFRPE)instacron:UFRPEORIGINALJorge Gustavo Bandeira dos Santos.pdfJorge Gustavo Bandeira dos Santos.pdfapplication/pdf964319http://www.tede2.ufrpe.br:8080/tede2/bitstream/tede2/8510/2/Jorge+Gustavo+Bandeira+dos+Santos.pdf6bbe56bd95fb1eb09406170addbbb499MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82165http://www.tede2.ufrpe.br:8080/tede2/bitstream/tede2/8510/1/license.txtbd3efa91386c1718a7f26a329fdcb468MD51tede2/85102020-10-13 18:25:03.521oai:tede2: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Biblioteca Digital de Teses e Dissertaçõeshttp://www.tede2.ufrpe.br:8080/tede/PUBhttp://www.tede2.ufrpe.br:8080/oai/requestbdtd@ufrpe.br ||bdtd@ufrpe.bropendoar:2024-05-28T12:37:05.543944Biblioteca Digital de Teses e Dissertações da UFRPE - Universidade Federal Rural de Pernambuco (UFRPE)false |
dc.title.por.fl_str_mv |
Criticalidade do modelo de Ising tridimensional : um estudo dinâmico |
title |
Criticalidade do modelo de Ising tridimensional : um estudo dinâmico |
spellingShingle |
Criticalidade do modelo de Ising tridimensional : um estudo dinâmico SANTOS, Jorge Gustavo Bandeira dos Modelo de Ising Dinâmica de Metropolis Magnetização CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Criticalidade do modelo de Ising tridimensional : um estudo dinâmico |
title_full |
Criticalidade do modelo de Ising tridimensional : um estudo dinâmico |
title_fullStr |
Criticalidade do modelo de Ising tridimensional : um estudo dinâmico |
title_full_unstemmed |
Criticalidade do modelo de Ising tridimensional : um estudo dinâmico |
title_sort |
Criticalidade do modelo de Ising tridimensional : um estudo dinâmico |
author |
SANTOS, Jorge Gustavo Bandeira dos |
author_facet |
SANTOS, Jorge Gustavo Bandeira dos |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
SOUZA, Adauto José Ferreira de |
dc.contributor.referee1.fl_str_mv |
ROMAGUERA, Antônio Rodrigues de Castro |
dc.contributor.referee2.fl_str_mv |
VILELA, André Luis da Mota |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/0227684644192779 |
dc.contributor.author.fl_str_mv |
SANTOS, Jorge Gustavo Bandeira dos |
contributor_str_mv |
SOUZA, Adauto José Ferreira de ROMAGUERA, Antônio Rodrigues de Castro VILELA, André Luis da Mota |
dc.subject.por.fl_str_mv |
Modelo de Ising Dinâmica de Metropolis Magnetização |
topic |
Modelo de Ising Dinâmica de Metropolis Magnetização CIENCIAS EXATAS E DA TERRA::FISICA |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::FISICA |
description |
In this work we investigate the criticality of the three-dimensional Ising model with interactions between rst neighbors. In our computational simulations we consider that the spins are distributed in a simple cubic lattice of side L, and lattice parameter a, so the number of spins in the lattice is N = (L=a)3. We employ periodical conditions of contour to describe the volumetric limit, in which the border and nite-size e ects are eliminated. We investigate the critical behavior of the system through the dynamic relaxation technique in short terms where the system evolves according to the Metropolis dynamic. Futhermore, the system properties are calculated before it reaches a state of equilibrium. Here, we consider only evolution from a completely ordered state, that is, the magnetization density of the system at the initial time is unitary. We calculate the magnetization (M), the structure factor (Sk), the time-dependent correlation length ( ), the uctuation of the order parameter (4m) and the second cumulante of Binder (U2). The value of the inverse of the critical temperature, Kc, was estimated using a method that explores the scale behavior of the derivative logarithm of the order parameter with respect to the logarithm of time (t; "), where " measures the distance to the critical point. The quantity (t; ") gives, besides the value of Kc, estimates for the critical exponents , and . The technique of data collapse is used for the purpose of obtaining greater accuracy in the values of the critical parameters obtained. The results found in this work for the critical parameter Kc = 0; 22166(3) and for the critical exponents = 0; 6495(3), = 1,2884(5) and = 0; 3222(3), were compared with others available in the recent specialized literature, for systems that are in the same class as the universality of the three-dimensional Ising model, in which we nd concordance until the fth decimal place through a technique that has a low computational requirement. |
publishDate |
2015 |
dc.date.issued.fl_str_mv |
2015-08-13 |
dc.date.accessioned.fl_str_mv |
2020-10-13T21:25:03Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SANTOS, Jorge Gustavo Bandeira dos. Criticalidade do modelo de Ising tridimensional : um estudo dinâmico. 2015. 59 f. Dissertação (Programa de Pós-Graduação em Física Aplicada) - Universidade Federal Rural de Pernambuco, Recife. |
dc.identifier.uri.fl_str_mv |
http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8510 |
identifier_str_mv |
SANTOS, Jorge Gustavo Bandeira dos. Criticalidade do modelo de Ising tridimensional : um estudo dinâmico. 2015. 59 f. Dissertação (Programa de Pós-Graduação em Física Aplicada) - Universidade Federal Rural de Pernambuco, Recife. |
url |
http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8510 |
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por |
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por |
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openAccess |
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Universidade Federal Rural de Pernambuco |
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Programa de Pós-Graduação em Física Aplicada |
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UFRPE |
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Universidade Federal Rural de Pernambuco |
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