Critical Decay at Higher-Order Glass-Transition Singularities

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: $\varphi (t)-f\propto {\sum }_i{g}_i(x)$, 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.

26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted)

References in corpus (4)

• Logarithmic Relaxation in Glass-Forming Systems
• Logarithmic Relaxation in a Colloidal System
• Dynamics in Colloidal Liquids near a Crossing of Glass- and Gel-Transition Lines
• Higher-order glass-transition singularities in systems with short-ranged attractive potentials

Cited by in corpus (2)

• Liquid-glass transition of a fluid confined in a disordered porous matrix: A mode-coupling theory
• Arrested phase separation in a short-ranged attractive colloidal system: A numerical study