Effect of particle exchange on the glass transition of binary hard spheres

We investigate the replica theory of the liquid-glass transition for a binary mixture of large and small additive hard spheres. We consider two different ans\"atze for this problem: the frozen glass ansatz (FGA) in whichs the exchange of large and small particles in a glass state is prohibited, and the exchange glass ansatz (EGA), in which it is allowed. We calculate the dynamical and thermodynamical glass transition points with the two ans\"atze. We show that the dynamical transition density of the FGA is lower than that of the EGA, while the thermodynamical transition density of the FGA is higher than that of the EGA. We discuss the algorithmic implications of these results for the density-dependence of the relaxation time of supercooled liquids. We particularly emphasize the difference between the standard Monte Carlo and swap Monte Carlo algorithms. Furthermore, we discuss the importance of particle exchange for estimating the configurational entropy.Comment: 16 pages, 5 figure

Dynamically correlated regions and configurational entropy in supercooled liquids

When a liquid is cooled below its melting temperature, if crystallization is avoided, it forms a glass. This phenomenon, called glass transition, is characterized by a marked increase of viscosity, about 14 orders of magnitude, in a narrow temperature interval. The microscopic mechanism behind the glass transition is still poorly understood. However, recently, great advances have been made in the identification of cooperative rearranging regions, or dynamical heterogeneities, i.e. domains of the liquid whose relaxation is highly correlated. The growth of the size of these domains is now believed to be the driving mechanism for the increase of the viscosity. Recently a tool to quantify the size of these domains has been proposed. We apply this tool to a wide class of materials to investigate the correlation between the size of the heterogeneities and their configurational entropy, i.e. the number of states accessible to a correlated domain. We find that the relaxation time of a given system, apart from a material dependent pre-factor, is a universal function of the configurational entropy of a correlated domain. As a consequence, we find that at the glass transition temperature, the size of the domains and the configurational entropy per unit volume are anti-correlated, as originally predicted by the Adam-Gibbs theory. Finally, we use our data to extract some exponents defined in the framework of the Random First Order Theory, a recent quantitative theory of the glass transition.Comment: 8 pages, 4 figures, 3 table

Comment to "Packing Hyperspheres in High-Dimensional Euclidean Space"

It is shown that the numerical data in cond-mat/0608362 are in very good agreement with the predictions of cond-mat/0601573.Comment: comment to cond-mat/0608362; 3 pages, 1 figur