Critical Decay at Higher-Order Glass-Transition Singularities

TL;DR

This paper analyzes the asymptotic behavior of density correlation functions near higher-order glass-transition singularities within mode-coupling theory, revealing a logarithmic decay pattern in various models.

Contribution

It introduces a novel asymptotic series expansion for correlation functions at A_3- and A_4-glass-transition singularities, applicable to schematic and colloid models.

Findings

Correlation functions follow a logarithmic decay series near singularities.

The asymptotic series is demonstrated in schematic models.

Results are extended to a colloid model with square-well interactions.

Abstract

Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A_3- and A_4-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: $\phi(t)-f\propto \sum_i g_i(x)$, where $g_n(x)=p_n(\ln x)/x^n$ with p_n denoting some polynomial and x=ln (t/t_0). The results are demonstrated for schematic models describing the system by solely one or two correlators and also for a colloid model with a square-well-interaction potential.