Critical decay at higher-order glass-transition singularities

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 A₃- and A₄-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: Φ(t) - f α σ_i g_i(x), where g_n(x) = p_n(ln x)/xⁿ with p_n denoting some polynomial and x = ln(t/t₀). 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.