Energy Landscape and Overlap Distribution of Binary Lennard-Jones Glasses

– We study the distribution of overlaps of glassy minima, taking proper care of residual symmetries of the system. Ensembles of locally stable, low lying glassy states are efficiently generated by rapid cooling from the liquid phase which has been equilibrated at a temperature Trun. Varying Trun, we observe a transition from a regime where a broad range of states are sampled to a regime where the system is almost always trapped in a metastable glassy state. We do not observe any structure in the distribution of overlaps of glassy minima, but find only very weak correlations, comparable in size to those of two liquid configurations. The phenomenology of supercooled liquids, the glass transition and the glassy phase have been related to results of analytical calculations for microscopic models of spin glasses [1, 2]. The latter bear no obvious relevance to structural glasses, hence, it is particularly important to see, whether the analogy can be supported quantitatively. One of the most prominent features of those spin-glass models, which have been put forward as models of structural glasses, is one step replica symmetry breaking, resulting in a bimodal distribution of overlaps between pure states. Generally speaking, one would expect to see non-trivial correlations among glassy states, if mean field theory of spin glasses were to apply. The liquid to glass transition as it is observed e.g. in metallic glasses, is a non-equilibrium phenomenon with the crystalline state being the true ground state. Glassy states are in general metastable states, sometimes called quasi-ergodic components, which are mutually inaccessible on experimental time scales, while equilibrium within a quasi-ergodic component is reached on much shorter time scales. In contrast to mean field models of spin glasses the ensemble of metastable states depends on the preparation method and the appropriate weights for metastable states are not unique. The assumption of an idealised preparation method, which cools the liquid arbitrarily slowly and at the same time prevents crystallization, has never been verified and seems contradictory to us. We therefore prefer to use a different idealised preparation ensemble which corresponds to infinitely rapid cooling from liquid equilibrium states. This method was first introduced by Stillinger and Weber [3, 4]. Typeset using EURO-TEX 2 EUROPHYSICS LETTERS Distance Measure in Configuration Space. – We study correlations among an ensemble of such metastable states, labelled by a. A glassy state a is characterized by a spontaneous breaking of translational invariance as signalled by a non-zero expectation value of the Fouriercomponents 〈exp (i~k~ri)〉a 6= 0 of the local density. Here ~ri denotes the position of the i-th particle, i = 1, . . . , N . The local density is analogous to the local magnetization, which is non-zero in the spin glass phase, 〈si〉a 6= 0, indicating the spontaneous breaking of the Ising symmetry. An overlap between two glassy configurations can be defined as