Transição de fase quântica e modelos de spins frustrados
Autor(a) principal: | |
---|---|
Data de Publicação: | 2007 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/9242 |
Resumo: | In this thesis, we will study the quantum phase transition of frustrated quantum spin models: (i) van Hemmen model ( S = 1) with transverse and anisotropic biaxial field (ii) Heisenberg model (S = 1/2 ) with competitive interaction first and second nearest neighbours (J1-J2 model) (iii) Ising model with transverse field and first magnetic model is studied to simulate the spin glass properties in real systems like the magnetic susceptibility cusp. We use the bimodal and gaussian probability distribution for random interactions. Applying the first-order approximation to decouple the products of exponential of operators, we calculate free energy and order parameter. Both, the transverse field and anisotropic transverse field destroy the spin glass order. In the second model, we use the effective field theory with differential operator technique and effective field renormalization group (EFRG) formalism. The phase diagrams are determined where are observe ferromagnetic (F), antiferromagnetic (AF) and superantiferromagnetic (SAF) states. In case of Heisenberg model in a square lattice at T=0, we have a quantum paramagnetic state that has been considered as a spin-liquid (SL) state in literature. For a simple cubic lattice, this spin-liquid state has not been observed. Which shows that the dimension of the system has influences on the quantum fluctuation at T=0. In the phase diagrams are the presence of first and second order phase transitions. Finally, are consider the critical behavior of the frustrated quantum Ising model and at T=0 we have the states with energy gap proportional to the transverse field intensity. Depending in the frustration parameter the system also shows first and second order transitions. |
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Azevedo, José Roberto VianaSousa, José Ricardo dehttp://lattes.cnpq.br/3871066069541626http://lattes.cnpq.br/7115884585420145431dd940-1c20-4fe7-96ef-23750c3cec722017-12-21T17:16:03Z2017-12-21T17:16:03Z2007-03-15AZEVEDO, José Roberto Viana. Transição de fase quântica e modelos de spins frustrados. 2007. Tese (Doutorado em Física) – Universidade Federal de São Carlos, São Carlos, 2007. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9242.https://repositorio.ufscar.br/handle/ufscar/9242In this thesis, we will study the quantum phase transition of frustrated quantum spin models: (i) van Hemmen model ( S = 1) with transverse and anisotropic biaxial field (ii) Heisenberg model (S = 1/2 ) with competitive interaction first and second nearest neighbours (J1-J2 model) (iii) Ising model with transverse field and first magnetic model is studied to simulate the spin glass properties in real systems like the magnetic susceptibility cusp. We use the bimodal and gaussian probability distribution for random interactions. Applying the first-order approximation to decouple the products of exponential of operators, we calculate free energy and order parameter. Both, the transverse field and anisotropic transverse field destroy the spin glass order. In the second model, we use the effective field theory with differential operator technique and effective field renormalization group (EFRG) formalism. The phase diagrams are determined where are observe ferromagnetic (F), antiferromagnetic (AF) and superantiferromagnetic (SAF) states. In case of Heisenberg model in a square lattice at T=0, we have a quantum paramagnetic state that has been considered as a spin-liquid (SL) state in literature. For a simple cubic lattice, this spin-liquid state has not been observed. Which shows that the dimension of the system has influences on the quantum fluctuation at T=0. In the phase diagrams are the presence of first and second order phase transitions. Finally, are consider the critical behavior of the frustrated quantum Ising model and at T=0 we have the states with energy gap proportional to the transverse field intensity. Depending in the frustration parameter the system also shows first and second order transitions.Nesta tese estudaremos a transição de fase quântica dos modelos de spins quânticos frustrados: i) Modelo de van Hemmen de spin S=1 com campo transverso e anisotropia biaxial; ii) modelo de Heisenberg de spin ½ anisotrópico com interações competitivas entre primeiros e segundos vizinhos (modelo J1-J2); iii) modelo de Ising com campo transverso e com interações de primeiros e segundos vizinhos. O primeiro modelo magnético é estudado para simular as propriedades de vidro de spin em sistemas reais, como, por exemplo, a cúspide da susceptibilidade magnética. Usamos as densidades de probabilidades bimodal e gaussiana nas ligações aleatórias. Aplicando a aproximação de primeira ordem para desacoplar o produto de exponenciais de operadores, calculamos a energia livre e parâmetro de ordem. Tanto o campo transverso quanto as anisotropias transversais, individualmente, atuam como agentes de destruição da ordem vidro de spin. Neste modelo são estudadas transições de fases quânticas de primeira e segunda ordem. No segundo modelo usamos o formalismo da teoria de campo efetivo via técnica do operador diferencial e grupo de renormalização na aproximação de campo efetivo (EFRG). São determinados diagramas de fases, onde observamos os estados ferromagnético (F), antiferromagnético (AF), superantiferromagnético (SAF) (denominado de colinear para uma rede quadrada e laminar para uma rede cúbica simples). No caso Heisenberg numa rede quadrada , em T=0 temos um estado paramagnético quântico que é sugerido a ser o estado spin-líquido (SL) discutido na literatura. Para a rede cúbica simples esse estado spin-líquido não foi observado, mostrando que o efeito da dimensionalidade no sistema influencia nas flutuações quânticas em T=0. Nos diagramas de fases temos as presenças de transições de primeira e segunda ordem. Finalmente, tratamos da criticalidade do modelo de Ising quântico frustrado, e em T=0 temos estados com gap de energia proporcional a intensidade do campo transverso, que dependendo do parâmetro de frustração o sistema presencia também transições de primeira e segunda ordem.Fundação de Amparo à Pesquisa do Estado do Amazonas (FAPEAM)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Física - PPGFUFSCarTransição de fase quânticaModelos de spins quânticos frustradosCIENCIAS EXATAS E DA TERRA::FISICATransição de fase quântica e modelos de spins frustradosinfo: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:UFSCARORIGINALAZEVEDO_José_2017.pdfAZEVEDO_José_2017.pdfapplication/pdf2048175https://repositorio.ufscar.br/bitstream/ufscar/9242/1/AZEVEDO_Jos%c3%a9_2017.pdf8f9c77b624ba3e310f344bcb798ee84dMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/9242/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTAZEVEDO_José_2017.pdf.txtAZEVEDO_José_2017.pdf.txtExtracted texttext/plain423509https://repositorio.ufscar.br/bitstream/ufscar/9242/3/AZEVEDO_Jos%c3%a9_2017.pdf.txt63e737db5f0697454236a64cd1be7928MD53THUMBNAILAZEVEDO_José_2017.pdf.jpgAZEVEDO_José_2017.pdf.jpgIM Thumbnailimage/jpeg7986https://repositorio.ufscar.br/bitstream/ufscar/9242/4/AZEVEDO_Jos%c3%a9_2017.pdf.jpg52037f3b29367f6cd66039a4fc0b5a35MD54ufscar/92422023-09-18 18:31:10.534oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:10Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Transição de fase quântica e modelos de spins frustrados |
title |
Transição de fase quântica e modelos de spins frustrados |
spellingShingle |
Transição de fase quântica e modelos de spins frustrados Azevedo, José Roberto Viana Transição de fase quântica Modelos de spins quânticos frustrados CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Transição de fase quântica e modelos de spins frustrados |
title_full |
Transição de fase quântica e modelos de spins frustrados |
title_fullStr |
Transição de fase quântica e modelos de spins frustrados |
title_full_unstemmed |
Transição de fase quântica e modelos de spins frustrados |
title_sort |
Transição de fase quântica e modelos de spins frustrados |
author |
Azevedo, José Roberto Viana |
author_facet |
Azevedo, José Roberto Viana |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/7115884585420145 |
dc.contributor.author.fl_str_mv |
Azevedo, José Roberto Viana |
dc.contributor.advisor1.fl_str_mv |
Sousa, José Ricardo de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/3871066069541626 |
dc.contributor.authorID.fl_str_mv |
431dd940-1c20-4fe7-96ef-23750c3cec72 |
contributor_str_mv |
Sousa, José Ricardo de |
dc.subject.por.fl_str_mv |
Transição de fase quântica Modelos de spins quânticos frustrados |
topic |
Transição de fase quântica Modelos de spins quânticos frustrados CIENCIAS EXATAS E DA TERRA::FISICA |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::FISICA |
description |
In this thesis, we will study the quantum phase transition of frustrated quantum spin models: (i) van Hemmen model ( S = 1) with transverse and anisotropic biaxial field (ii) Heisenberg model (S = 1/2 ) with competitive interaction first and second nearest neighbours (J1-J2 model) (iii) Ising model with transverse field and first magnetic model is studied to simulate the spin glass properties in real systems like the magnetic susceptibility cusp. We use the bimodal and gaussian probability distribution for random interactions. Applying the first-order approximation to decouple the products of exponential of operators, we calculate free energy and order parameter. Both, the transverse field and anisotropic transverse field destroy the spin glass order. In the second model, we use the effective field theory with differential operator technique and effective field renormalization group (EFRG) formalism. The phase diagrams are determined where are observe ferromagnetic (F), antiferromagnetic (AF) and superantiferromagnetic (SAF) states. In case of Heisenberg model in a square lattice at T=0, we have a quantum paramagnetic state that has been considered as a spin-liquid (SL) state in literature. For a simple cubic lattice, this spin-liquid state has not been observed. Which shows that the dimension of the system has influences on the quantum fluctuation at T=0. In the phase diagrams are the presence of first and second order phase transitions. Finally, are consider the critical behavior of the frustrated quantum Ising model and at T=0 we have the states with energy gap proportional to the transverse field intensity. Depending in the frustration parameter the system also shows first and second order transitions. |
publishDate |
2007 |
dc.date.issued.fl_str_mv |
2007-03-15 |
dc.date.accessioned.fl_str_mv |
2017-12-21T17:16:03Z |
dc.date.available.fl_str_mv |
2017-12-21T17:16:03Z |
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 |
AZEVEDO, José Roberto Viana. Transição de fase quântica e modelos de spins frustrados. 2007. Tese (Doutorado em Física) – Universidade Federal de São Carlos, São Carlos, 2007. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9242. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/9242 |
identifier_str_mv |
AZEVEDO, José Roberto Viana. Transição de fase quântica e modelos de spins frustrados. 2007. Tese (Doutorado em Física) – Universidade Federal de São Carlos, São Carlos, 2007. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9242. |
url |
https://repositorio.ufscar.br/handle/ufscar/9242 |
dc.language.iso.fl_str_mv |
por |
language |
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 |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
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