Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/150383 |
Resumo: | The behavior of the nonlinear susceptibility χ3 and its relation to the spin-glass transition temperature Tf in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature Tf can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at Tf , which comes as a direct consequence of λAT = 0 at Tf. However, our results show that, in the presence of random fields, χ3 presents a rounded maximum at a temperature T * which does not coincide with the spin-glass transition temperature Tf (i.e., T * > Tf for a given applied random field). Thus, the maximum value of χ3 at T * reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that χ3 still maintains a dependence on the replicon λAT, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the LiHoxY1−xF4 compound. |
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Morais Junior, Carlos Alberto Vaz deZimmer, Fábio MallmannLazo, Matheus JatkoskeMagalhaes, Sergio GarciaNobre, Fernando Dantas2016-12-31T02:21:35Z20160163-1829http://hdl.handle.net/10183/150383001008287The behavior of the nonlinear susceptibility χ3 and its relation to the spin-glass transition temperature Tf in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature Tf can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at Tf , which comes as a direct consequence of λAT = 0 at Tf. However, our results show that, in the presence of random fields, χ3 presents a rounded maximum at a temperature T * which does not coincide with the spin-glass transition temperature Tf (i.e., T * > Tf for a given applied random field). Thus, the maximum value of χ3 at T * reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that χ3 still maintains a dependence on the replicon λAT, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the LiHoxY1−xF4 compound.application/pdfengPhysical review. New York. Vol. 93, no. 22 (June 2016), 224206, 6 p.Vidros de spinTransformações de faseCampos aleatóriosSuscetibilidade magnéticaSpin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fieldsEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL001008287.pdf001008287.pdfTexto completo (inglês)application/pdf499447http://www.lume.ufrgs.br/bitstream/10183/150383/1/001008287.pdfd58c731aa54c0058215cd28a19bad963MD51TEXT001008287.pdf.txt001008287.pdf.txtExtracted Texttext/plain29847http://www.lume.ufrgs.br/bitstream/10183/150383/2/001008287.pdf.txt49911935cb201072044793053f54c1deMD52THUMBNAIL001008287.pdf.jpg001008287.pdf.jpgGenerated Thumbnailimage/jpeg2168http://www.lume.ufrgs.br/bitstream/10183/150383/3/001008287.pdf.jpgcd4d28b1e492618b19b17ea9789a45fbMD5310183/1503832018-10-30 07:56:48.796oai:www.lume.ufrgs.br:10183/150383Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2018-10-30T10:56:48Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields |
title |
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields |
spellingShingle |
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields Morais Junior, Carlos Alberto Vaz de Vidros de spin Transformações de fase Campos aleatórios Suscetibilidade magnética |
title_short |
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields |
title_full |
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields |
title_fullStr |
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields |
title_full_unstemmed |
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields |
title_sort |
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields |
author |
Morais Junior, Carlos Alberto Vaz de |
author_facet |
Morais Junior, Carlos Alberto Vaz de Zimmer, Fábio Mallmann Lazo, Matheus Jatkoske Magalhaes, Sergio Garcia Nobre, Fernando Dantas |
author_role |
author |
author2 |
Zimmer, Fábio Mallmann Lazo, Matheus Jatkoske Magalhaes, Sergio Garcia Nobre, Fernando Dantas |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Morais Junior, Carlos Alberto Vaz de Zimmer, Fábio Mallmann Lazo, Matheus Jatkoske Magalhaes, Sergio Garcia Nobre, Fernando Dantas |
dc.subject.por.fl_str_mv |
Vidros de spin Transformações de fase Campos aleatórios Suscetibilidade magnética |
topic |
Vidros de spin Transformações de fase Campos aleatórios Suscetibilidade magnética |
description |
The behavior of the nonlinear susceptibility χ3 and its relation to the spin-glass transition temperature Tf in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature Tf can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at Tf , which comes as a direct consequence of λAT = 0 at Tf. However, our results show that, in the presence of random fields, χ3 presents a rounded maximum at a temperature T * which does not coincide with the spin-glass transition temperature Tf (i.e., T * > Tf for a given applied random field). Thus, the maximum value of χ3 at T * reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that χ3 still maintains a dependence on the replicon λAT, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the LiHoxY1−xF4 compound. |
publishDate |
2016 |
dc.date.accessioned.fl_str_mv |
2016-12-31T02:21:35Z |
dc.date.issued.fl_str_mv |
2016 |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
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0163-1829 |
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001008287 |
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http://hdl.handle.net/10183/150383 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical review. New York. Vol. 93, no. 22 (June 2016), 224206, 6 p. |
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info:eu-repo/semantics/openAccess |
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openAccess |
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