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Monte Carlo algorithms such as the Wang-Landau algorithm and similar`entropic' methods are able to accurately sample the density of states of modelsystems and thereby give access to thermal equilibrium properties at anytemperature. Thermal equilibrium is however not achievable at low temperaturesin glassy systems. Such systems are characterized by a multitude of metastableconfigurations, pictorially referred to as `valleys' of an energy landscape.Geometrical properties of the landscape, e.g. the local density of statesdescribing the distribution in energy of the states belonging to a singlevalley, are key to understand the dynamical properties of such systems. In thispaper we combine the lid algorithm, a tool for landscape exploration previouslyapplied to a range of models, with the Wang-Swendsen algorithm. To test thisimproved exploration tool, we consider a paradigmatic complex system, theEdwards-Andersom model in two and three spatial dimension. We find a strikingdifference between the energy dependence of the local density of states in thetwo cases: nearly flat in the first case, and nearly exponential in the second.The lid dependence of the data is analyzed to estimate the form of the globaldensity of states.

Entropic algorithms and the lid method as exploration tools for complex landscapes