Critical Decay at Higher-Order Glass-Transition Singularities

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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∝ ∑ᵢ gᵢ(x), where gₙ(x)=pₙ(x)/xⁿ with pₙ 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.