Higher order glass-transition singularities in colloidal systems with attractive interactions

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The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line, and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third order bifurcation point, i.e. in a A₃ (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth order A₄ (swallow-tail) singularity at a critical well width. Close to the A₃ and A₄ singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.