Dynamic glass transition: Bridging the gap between mode-coupling theory and the replica approach

Department of Chemistry, Colorado State University - Fort Collins, CO 80523, USA

^a grzegorz.szamel@colostate.edu

Received: 11 June 2010
Accepted: 16 August 2010

Abstract

We clarify the relation between the ergodicity-breaking transition predicted by the mode-coupling theory and the so-called dynamic transition predicted by the static replica approach. Following Franz and Parisi (Phys. Rev. Lett., 79 (1997) 2486), we consider a system of particles in a metastable state characterized by non-trivial correlations with a quenched configuration. We show that the assumption that in a metastable state particle currents vanish leads to an expression for the replica off-diagonal direct correlation function in terms of a non-trivial part of the replica off-diagonal static four-point correlation function. A factorization approximation for this function results in an approximate closure for the replica off-diagonal direct correlation function. The replica off-diagonal Ornstein-Zernicke equation combined with this closure coincides with the equation for the non-ergodicity parameter derived using the mode-coupling theory.