Real space analysis of inherent structures
نویسنده
چکیده
– We study a generalization of the one-dimensional disordered Potts model, which exhibits glassy properties at low temperature. The real space properties of inherent structures visited dynamically are analyzed through a decomposition into domains over which the energy is minimized. The size of these domains is distributed exponentially, defining a characteristic length scale which grows when lowering temperature. This length can be interpreted within a simple picture in terms of defects on top of the ground state. The existence of a length scale which grows when approaching the glass transition in disordered systems has been the subject of intense numerical studies in the past decade, both in equilibrium [1,2] or in the aging regime [3–6], since this length is a key ingredient to understand the divergence of the relaxation time. Some indirect experimental evidence for such a length scale has also been found [7]. As the presence of disorder renders useless the usual two-point correlation fonctions, new tools, like the two-replica (four-point) correlation function, have been developed to measure a characteristic length scale. This correlation function compares the dynamical state of two copies of the system having the same disorder, but independent thermal histories. The ‘two-replica’ coherence length has also been shown to display important links with the scaling properties of other measurable quantities [8]. However, from a physical point of view, such a length scale remains difficult to interpret: what are the role of metastable states and of the minimization of energy in the growth of this typical length? Indeed, glasses are known to have an exponentially large (with the system size) number of metastable states [9], often called inherent structures (IS) in this context. IS are defined as local minima of the potential energy in phase space, i.e. they are stable against a set of elementary transitions defined by the dynamical rules [10–12]. This notion has been shown to be extremely useful for the understanding of glassy dynamics, both in disordered [13, 14] and non disordered systems [15, 16]. From a real space point of view, examples of spatial analysis of IS are known for long –see e.g. [17] for the disordered Ising chain– but this analysis was considered as a technical procedure to compute the configurational entropy rather than a way to introduce a characteristic length scale. The issue of characteristic length scales for IS was addressed recently in the context of kinetically constrained models (models with no interactions, but with kinetic constraints), where IS are found to differ from the ground state
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