title: Dynamical transition of glasses: from exact to approximate.
abstract: We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is exactly described by equations conceptually close, but different from, the mode-coupling equations. We obtain these by a dynamic virial construction. Quite surprisingly, we observe that in three dimensions, the mean-field behavior is closely followed for ranges as small as one interparticle distance, and still qualitatively for smaller distances. For the original particle model, we expect the present mean-field theory to become, unlike the mode-coupling equations, an increasingly good approximation at higher dimensions.
authors.affiliation: PMMH, CNRS, ESPCI-ParisTech, UMR 7636, 10 rue Vauquelin, 75231 Paris Cedex 05, France. mari@pmmh.espci.fr
authors.forename: Romain
authors.initials: R
authors.lastname: Mari
authors.forename: Jorge
authors.initials: J
authors.lastname: Kurchan