Damage spreading transition in glasses: A probe for the ruggedness of the configurational landscape
We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of metastable states. For systems evolving und...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1999 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/18877 |
| Acceso en línea: | https://hdl.handle.net/2445/18877 |
| Access Level: | acceso abierto |
| Palabra clave: | Física estadística Termodinàmica Sistemes no lineals Propietats magnètiques Equacions d'estat Regla de les fases i equilibri Transformacions de fase (Física estadística) Statistical physics Thermodynamics Nonlinear systems Magnetic properties Equations of state Phase rule and equilibrium Phase transformations (Statistical physics) |
| Sumario: | We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of metastable states. For systems evolving under identical but arbitrarily correlated noises, we demonstrate that there exists a critical temperature T0 which separates two different dynamical regimes depending on whether damage spreads or not in the asymptotic long-time limit. This transition exists for generic noise correlations such that the zero damage solution is stable at high temperatures, being minimal for maximal noise correlations. Although this dynamical transition depends on the type of noise correlations, we show that the asymptotic damage has the good properties of a dynamical order parameter, such as (i) independence of the initial damage; (ii) independence of the class of initial condition; and (iii) stability of the transition in the presence of asymmetric interactions which violate detailed balance. For maximally correlated noises we suggest that damage spreading occurs due to the presence of a divergent number of saddle points (as well as metastable states) in the thermodynamic limit consequence of the ruggedness of the free-energy landscape which characterizes the glassy state. These results are then compared to extensive numerical simulations of a mean-field glass model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom of choosing arbitrary noise correlations for Langevin dynamics makes damage spreading an interesting tool to probe the ruggedness of the configurational landscape. |
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