Glassy behaviour in a simple topological model
In this paper we study a simple, purely topological, cellular model which is allowed to evolve through a Glauber-Kawasaki process. We find a non-thermodynamic transition to a glassy phase in which the energy (defined as the square of the local cell topological charge) fails to reach the equilibrium...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2000
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| _version_ | 1797079095227449344 |
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| author | Davison, L Sherrington, D |
| author_facet | Davison, L Sherrington, D |
| author_sort | Davison, L |
| collection | OXFORD |
| description | In this paper we study a simple, purely topological, cellular model which is allowed to evolve through a Glauber-Kawasaki process. We find a non-thermodynamic transition to a glassy phase in which the energy (defined as the square of the local cell topological charge) fails to reach the equilibrium value below a characteristic temperature which is dependent on the cooling rate. We investigate a correlation function which exhibits ageing behaviour, and follows a master curve in the stationary regime when time is rescaled by a factor of the relaxation time tr. This master curve can be fitted by a von Schweidler law in the late β-relaxation regime. The relaxation times can be well fitted at all temperatures by an offset Arrhenius law. A power law can be fitted to an intermediate-temperature regime; the exponent of the power law and the von Schweidler law roughly agree with the relationship predicted by mode-coupling theory. By defining a suitable response function, we find that the fluctuation-dissipation ratio is held until sometime later than the appearance of the plateaux; non-monotonicity of the response is observed after this ratio is broken, a feature which has been observed in other models with dynamics involving activated processes. |
| first_indexed | 2024-03-07T00:40:48Z |
| format | Journal article |
| id | oxford-uuid:82f8b214-0dd3-4389-9ad2-d08d1f761dfc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:40:48Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:82f8b214-0dd3-4389-9ad2-d08d1f761dfc2022-03-26T21:41:04ZGlassy behaviour in a simple topological modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:82f8b214-0dd3-4389-9ad2-d08d1f761dfcEnglishSymplectic Elements at Oxford2000Davison, LSherrington, DIn this paper we study a simple, purely topological, cellular model which is allowed to evolve through a Glauber-Kawasaki process. We find a non-thermodynamic transition to a glassy phase in which the energy (defined as the square of the local cell topological charge) fails to reach the equilibrium value below a characteristic temperature which is dependent on the cooling rate. We investigate a correlation function which exhibits ageing behaviour, and follows a master curve in the stationary regime when time is rescaled by a factor of the relaxation time tr. This master curve can be fitted by a von Schweidler law in the late β-relaxation regime. The relaxation times can be well fitted at all temperatures by an offset Arrhenius law. A power law can be fitted to an intermediate-temperature regime; the exponent of the power law and the von Schweidler law roughly agree with the relationship predicted by mode-coupling theory. By defining a suitable response function, we find that the fluctuation-dissipation ratio is held until sometime later than the appearance of the plateaux; non-monotonicity of the response is observed after this ratio is broken, a feature which has been observed in other models with dynamics involving activated processes. |
| spellingShingle | Davison, L Sherrington, D Glassy behaviour in a simple topological model |
| title | Glassy behaviour in a simple topological model |
| title_full | Glassy behaviour in a simple topological model |
| title_fullStr | Glassy behaviour in a simple topological model |
| title_full_unstemmed | Glassy behaviour in a simple topological model |
| title_short | Glassy behaviour in a simple topological model |
| title_sort | glassy behaviour in a simple topological model |
| work_keys_str_mv | AT davisonl glassybehaviourinasimpletopologicalmodel AT sherringtond glassybehaviourinasimpletopologicalmodel |