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 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 proportional to Sigma(i) g(i)(x), where g(n)(x) = p(n)(Inx)/x(n) with p(n) denoting some polynomial and x = In(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.