Higher-order glass-transition singularities in systems with short-ranged attractive potentials

Within the mode-coupling theory for the evolution of structural relaxation, the A₄-glass-transition singularities are identified for systems of particles interacting with a hard-sphere repulsion complemented by different short-ranged potentials: Baxter's singular potential regularized by a large-wavevector cut-off, a model for the Asakura–Oosawa depletion attraction, a triangular potential, a Yukawa attraction, and a square-well potential. The regular potentials yield critical packing fractions, critical Debye–Waller factors, and critical amplitudes very close to each other. The elastic moduli and the particle localization lengths for corresponding states of the Yukawa system and the square-well system may differ by up to 20 and 10%, respectively.