Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada
Ano de defesa: | 2023 |
---|---|
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/1/28128 |
Resumo: | In the present work, we investigate the phase transitions of the Ising model with interactions between first (J1), second (J2) and third (J3) neighbours in the square lattice with transverse magnetic field. In this study, we adopt antiferromagnetic interactions between first and second neighbours and consider third-neighbours interactions to be both ferromagnetic and antiferromagnetic. The description of the classical and quantum phase transitions of the model is carried out by adopting the cluster mean-field approximation with four sites. As a result, we identified that strong enough third-neighbor interactions lead to the disappearance of tricriticality at the boundary between the superantiferromagnetic (SAF) and paramagnetic (PM) phases. In particular, tricriticality is more sensitive to the presence of ferromagnetic interactions, disappearing for |J3| ă 0.3|J1| in the absence of transverse field. In the presence of antiferromagnetic J3, we find first-order transitions between the degenerate staggered dimer phase and the PM phase. Furthermore, we find a change in the nature of the SAF-PM phase transitions introduced by quantum fluctuations. This phenomenon, called quantum annealed criticality (QAC), consists of classical first-order phase transitions that become second-order phase transitions in the presence of a strong enough transverse field. Our results allow establishing a range of parameters J2 and J3 for which it is possible to find QAC. The analysis of the model criticality allows concluding that a strong enough J3 interaction eliminates the QAC phenomenon. Therefore, our results suggest that attempts to realize QAC in a square lattice system should avoid strong interactions between third neighbors, mainly if these interactions are ferromagnetic. |
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spelling |
2023-03-09T12:14:47Z2023-03-09T12:14:47Z2023-02-14http://repositorio.ufsm.br/handle/1/28128In the present work, we investigate the phase transitions of the Ising model with interactions between first (J1), second (J2) and third (J3) neighbours in the square lattice with transverse magnetic field. In this study, we adopt antiferromagnetic interactions between first and second neighbours and consider third-neighbours interactions to be both ferromagnetic and antiferromagnetic. The description of the classical and quantum phase transitions of the model is carried out by adopting the cluster mean-field approximation with four sites. As a result, we identified that strong enough third-neighbor interactions lead to the disappearance of tricriticality at the boundary between the superantiferromagnetic (SAF) and paramagnetic (PM) phases. In particular, tricriticality is more sensitive to the presence of ferromagnetic interactions, disappearing for |J3| ă 0.3|J1| in the absence of transverse field. In the presence of antiferromagnetic J3, we find first-order transitions between the degenerate staggered dimer phase and the PM phase. Furthermore, we find a change in the nature of the SAF-PM phase transitions introduced by quantum fluctuations. This phenomenon, called quantum annealed criticality (QAC), consists of classical first-order phase transitions that become second-order phase transitions in the presence of a strong enough transverse field. Our results allow establishing a range of parameters J2 and J3 for which it is possible to find QAC. The analysis of the model criticality allows concluding that a strong enough J3 interaction eliminates the QAC phenomenon. Therefore, our results suggest that attempts to realize QAC in a square lattice system should avoid strong interactions between third neighbors, mainly if these interactions are ferromagnetic.No presente trabalho, investigamos as transições de fase do modelo de Ising com interações entre primeiros (J1), segundos (J2) e terceiros (J3) vizinhos na rede quadrada com campo magnético transverso. Neste estudo, adotamos interações antiferromagnéticas entre primeiros e segundos vizinhos e consideramos os casos com J3 ferromagnético e antiferromagnético. A descrição das transições de fase clássicas e quânticas do modelo foi realizada adotando a teoria de campo médio com clusters em uma aproximação com 4 sítios. Como resultado, identificamos que interações entre terceiros vizinhos intensas o suficiente levam ao desaparecimento da tricriticalidade na fronteira entre as fases superantiferromagnética (SAF) e paramagnética (PM). Em particular, a tricriticalidade é mais sensível à presença de interações ferromagnéticas, desaparecendo para |J3| ă 0.3|J1| na ausência de campo transverso. Na presença de interações entre terceiros vizinhos antiferromagnéticas, encontramos transições de primeira ordem entre a fase degenerada staggered dimer e a fase PM. Além disso, encontramos uma mudança na natureza das transições de fase SAF-PM introduzida por flutuações quânticas. Este fenômeno, chamado de quantum annealed criticality (QAC), consiste em transições de fase clássicas de primeira ordem que passam a ser de segunda ordem na presença de um campo transverso forte o suficiente. Nossos resultados permitem estabelecer um espectro de parâmetros J2 e J3 para os quais é possível encontrar o fenômeno QAC. A análise da criticalidade do modelo permite concluir que uma interação J3 forte o suficiente elimina o fenômeno QAC. Portanto, nossos resultados sugerem que tentativas de realizar experimentalmente o fenômeno QAC em um sistema com estrutura de rede quadrada devem evitar interações fortes entre terceiros vizinhos, especialmente se estas interações forem ferromagnéticas.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade 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/openAccessModelo de Ising quânticoFrustraçãoQuantum Ising modelQuantum annealed criticalityFrustrationCNPQ::CIENCIAS EXATAS E DA TERRA::FISICAEfeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustradaEffects of third-neighbour interactions on the criticality of the quantum Ising model on the frustrated square latticeinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisSchmidt, Mateushttp://lattes.cnpq.br/7494768123165528Piquini, Paulo CesarErichsen Junior, Rubemhttp://lattes.cnpq.br/4132493493676443Oliveira, Matheus Roos de100500000006600600600600600c43c4f80-f4d7-456d-abbe-040d1ba8c4dabe171939-b863-4857-b51e-d3f0182de411c0a8e987-39e6-4724-98f5-457bc3ee6bf0eaa9212b-b09e-42b0-939b-aedcf5611feereponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGFISICA_2023_OLIVEIRA_MATHEUS.pdfDIS_PPGFISICA_2023_OLIVEIRA_MATHEUS.pdfDissertação de Mestradoapplication/pdf692305http://repositorio.ufsm.br/bitstream/1/28128/1/DIS_PPGFISICA_2023_OLIVEIRA_MATHEUS.pdf524853d4dac2747b7b8c1c94e0325ceeMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.ufsm.br/bitstream/1/28128/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81956http://repositorio.ufsm.br/bitstream/1/28128/3/license.txt2f0571ecee68693bd5cd3f17c1e075dfMD531/281282023-03-09 09:14:47.125oai:repositorio.ufsm.br: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ório Institucionalhttp://repositorio.ufsm.br/PUBhttp://repositorio.ufsm.br/oai/requestopendoar:39132023-03-09T12:14:47Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.por.fl_str_mv |
Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada |
dc.title.alternative.eng.fl_str_mv |
Effects of third-neighbour interactions on the criticality of the quantum Ising model on the frustrated square lattice |
title |
Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada |
spellingShingle |
Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada Oliveira, Matheus Roos de Modelo de Ising quântico Frustração Quantum Ising model Quantum annealed criticality Frustration CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada |
title_full |
Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada |
title_fullStr |
Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada |
title_full_unstemmed |
Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada |
title_sort |
Efeitos de interações de terceiros vizinhos sobre a criticalidade do modelo de Ising quântico na rede quadrada frustrada |
author |
Oliveira, Matheus Roos de |
author_facet |
Oliveira, Matheus Roos de |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Schmidt, Mateus |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/7494768123165528 |
dc.contributor.referee1.fl_str_mv |
Piquini, Paulo Cesar |
dc.contributor.referee2.fl_str_mv |
Erichsen Junior, Rubem |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/4132493493676443 |
dc.contributor.author.fl_str_mv |
Oliveira, Matheus Roos de |
contributor_str_mv |
Schmidt, Mateus Piquini, Paulo Cesar Erichsen Junior, Rubem |
dc.subject.por.fl_str_mv |
Modelo de Ising quântico Frustração |
topic |
Modelo de Ising quântico Frustração Quantum Ising model Quantum annealed criticality Frustration CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
dc.subject.eng.fl_str_mv |
Quantum Ising model Quantum annealed criticality Frustration |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
description |
In the present work, we investigate the phase transitions of the Ising model with interactions between first (J1), second (J2) and third (J3) neighbours in the square lattice with transverse magnetic field. In this study, we adopt antiferromagnetic interactions between first and second neighbours and consider third-neighbours interactions to be both ferromagnetic and antiferromagnetic. The description of the classical and quantum phase transitions of the model is carried out by adopting the cluster mean-field approximation with four sites. As a result, we identified that strong enough third-neighbor interactions lead to the disappearance of tricriticality at the boundary between the superantiferromagnetic (SAF) and paramagnetic (PM) phases. In particular, tricriticality is more sensitive to the presence of ferromagnetic interactions, disappearing for |J3| ă 0.3|J1| in the absence of transverse field. In the presence of antiferromagnetic J3, we find first-order transitions between the degenerate staggered dimer phase and the PM phase. Furthermore, we find a change in the nature of the SAF-PM phase transitions introduced by quantum fluctuations. This phenomenon, called quantum annealed criticality (QAC), consists of classical first-order phase transitions that become second-order phase transitions in the presence of a strong enough transverse field. Our results allow establishing a range of parameters J2 and J3 for which it is possible to find QAC. The analysis of the model criticality allows concluding that a strong enough J3 interaction eliminates the QAC phenomenon. Therefore, our results suggest that attempts to realize QAC in a square lattice system should avoid strong interactions between third neighbors, mainly if these interactions are ferromagnetic. |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-03-09T12:14:47Z |
dc.date.available.fl_str_mv |
2023-03-09T12:14:47Z |
dc.date.issued.fl_str_mv |
2023-02-14 |
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/1/28128 |
url |
http://repositorio.ufsm.br/handle/1/28128 |
dc.language.iso.fl_str_mv |
por |
language |
por |
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100500000006 |
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600 600 600 600 600 |
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Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
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Programa de Pós-Graduação em Física |
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UFSM |
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Brasil |
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Física |
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Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
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