Logarithmic decay in a two-component model

TL;DR

This paper analyzes the decay behavior of correlation functions near higher-order glass-transition singularities in a two-component mode-coupling model, revealing logarithmic decay patterns and Vogel-Fulcher type scaling of the time scale.

Contribution

It introduces a detailed description of correlation decay and correction patterns near higher-order singularities within a schematic two-component mode-coupling model.

Findings

Correlation functions decay logarithmically near singularities

Leading correction causes convex and concave decay patterns

Time scale follows Vogel-Fulcher law close to singularities

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 $-\ln(t/\tau)$ and the leading correction introduces characteristic convex and concave patterns in the decay curves. The time scale $\tau$ follows a Vogel-Fulcher type law close to the higher-order singularities.