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)

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• Arrested phase separation in a short-ranged attractive colloidal system: A numerical study
• Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
• Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions
• Shape of Dynamical Heterogeneities and the Stokes-Einstein and Stokes-Einstein-Debye Relations in Suspensions of Colloidal Ellipsoids
• Glass glass transition and new dynamical singularity points in an analytically solvable p-spin glass like model
• Waiting-time dependent non-equilibrium phase diagram of simple glass- and gel-forming liquids
• Higher-Order Singularities without Glass-Glass Transitions