Logarithmic decay in a two-component model

Abstract

The correlation functions near higher-order glass-transition singularities are discussed for a schematic two-component model within the mode-coupling theory for ideal glass-transitions. The correlators decay in leading order like $-\ln(t/τ)$ and the leading correction introduces characteristic convex and concave patterns in the decay curves. The time scale $τ$ follows a Vogel-Fulcher type law close to the higher-order singularities.