Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/253119 |
Resumo: | After a sudden quench from the disordered high-temperature T0 → ∞ phase to a final temperature well below the critical point TF Tc, the nonconserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time tp1 > 0) and stabilization (at time tp > tp1 ) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, to study their role on each time regime after the quench (TF = 0), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability p. We show that observables such as the cluster size heterogeneity H(t, p) and the typical domain size (t, p) have no dependence on p in the first time regime up to tp1 . Furthermore, when energy-decreasing flips are forbidden while allowing constant-energy flips, the kinetics is essentially frozen after the quench and there is no percolation event whatsoever. Taken together, these results indicate that the emergence of the first percolating cluster at tp1 is completely driven by energy decreasing flips. However, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: tp(p) ∼ p−1 for p 1 (at p = 0, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and eff Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, tp1 and tp in such systems. |
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Lopes, Amanda de AzevedoAlmeida, Renan A. L.Oliveira, Paulo Murilo Castro deArenzon, Jeferson Jacob2022-12-24T05:04:20Z20221539-3755http://hdl.handle.net/10183/253119001157814After a sudden quench from the disordered high-temperature T0 → ∞ phase to a final temperature well below the critical point TF Tc, the nonconserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time tp1 > 0) and stabilization (at time tp > tp1 ) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, to study their role on each time regime after the quench (TF = 0), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability p. We show that observables such as the cluster size heterogeneity H(t, p) and the typical domain size (t, p) have no dependence on p in the first time regime up to tp1 . Furthermore, when energy-decreasing flips are forbidden while allowing constant-energy flips, the kinetics is essentially frozen after the quench and there is no percolation event whatsoever. Taken together, these results indicate that the emergence of the first percolating cluster at tp1 is completely driven by energy decreasing flips. However, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: tp(p) ∼ p−1 for p 1 (at p = 0, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and eff Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, tp1 and tp in such systems.application/pdfengPhysical review. E, Statistical, nonlinear, and soft matter physics. Melville. Vol. 106, no. 4 (Oct. 2022), 044105, 6 p.Modelo de isingPercolaçãoDinâmica de spinEnergy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising modelEstrangeiroinfo: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:UFRGSTEXT001157814.pdf.txt001157814.pdf.txtExtracted Texttext/plain34752http://www.lume.ufrgs.br/bitstream/10183/253119/2/001157814.pdf.txt5378492b20e86e1f23d24f4b3a110ff8MD52ORIGINAL001157814.pdfTexto completo (inglês)application/pdf551271http://www.lume.ufrgs.br/bitstream/10183/253119/1/001157814.pdfe46e72babba750233369f24a55092de5MD5110183/2531192024-03-28 06:21:56.820173oai:www.lume.ufrgs.br:10183/253119Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2024-03-28T09:21:56Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model |
title |
Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model |
spellingShingle |
Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model Lopes, Amanda de Azevedo Modelo de ising Percolação Dinâmica de spin |
title_short |
Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model |
title_full |
Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model |
title_fullStr |
Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model |
title_full_unstemmed |
Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model |
title_sort |
Energy-lowering and constant-energy spin flips : emergence of the percolating cluster in the kinetic Ising model |
author |
Lopes, Amanda de Azevedo |
author_facet |
Lopes, Amanda de Azevedo Almeida, Renan A. L. Oliveira, Paulo Murilo Castro de Arenzon, Jeferson Jacob |
author_role |
author |
author2 |
Almeida, Renan A. L. Oliveira, Paulo Murilo Castro de Arenzon, Jeferson Jacob |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Lopes, Amanda de Azevedo Almeida, Renan A. L. Oliveira, Paulo Murilo Castro de Arenzon, Jeferson Jacob |
dc.subject.por.fl_str_mv |
Modelo de ising Percolação Dinâmica de spin |
topic |
Modelo de ising Percolação Dinâmica de spin |
description |
After a sudden quench from the disordered high-temperature T0 → ∞ phase to a final temperature well below the critical point TF Tc, the nonconserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time tp1 > 0) and stabilization (at time tp > tp1 ) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, to study their role on each time regime after the quench (TF = 0), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability p. We show that observables such as the cluster size heterogeneity H(t, p) and the typical domain size (t, p) have no dependence on p in the first time regime up to tp1 . Furthermore, when energy-decreasing flips are forbidden while allowing constant-energy flips, the kinetics is essentially frozen after the quench and there is no percolation event whatsoever. Taken together, these results indicate that the emergence of the first percolating cluster at tp1 is completely driven by energy decreasing flips. However, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: tp(p) ∼ p−1 for p 1 (at p = 0, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and eff Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, tp1 and tp in such systems. |
publishDate |
2022 |
dc.date.accessioned.fl_str_mv |
2022-12-24T05:04:20Z |
dc.date.issued.fl_str_mv |
2022 |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/253119 |
dc.identifier.issn.pt_BR.fl_str_mv |
1539-3755 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001157814 |
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url |
http://hdl.handle.net/10183/253119 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical review. E, Statistical, nonlinear, and soft matter physics. Melville. Vol. 106, no. 4 (Oct. 2022), 044105, 6 p. |
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info:eu-repo/semantics/openAccess |
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openAccess |
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