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

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 $A_3$ (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth-order $A_4$ (swallow-tail) singularity at a critical well width. Close to the $A_3$ and $A_4$ singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.