Multiple higher-order singularities and iso-dynamics in a simple glass-former model

We investigate the slow dynamics of a colloidal model with two repulsive length scales, whose interaction potential is the sum of a hard-core and a square shoulder. Despite the simplicity of the interactions, Mode-Coupling theory predicts a complex dynamic scenario: a fluid-glass line with two reentrances and a glass-glass line ending with multiple higher-order ($A_3$ or $A_4$) singularities. In this work we verify the existence of the two $A_4$ points by numerical simulations, observing subdiffusive behaviour of the mean-square displacement and logarithmic decay of the density correlators. Surprisingly, we also discover a novel dynamic behaviour generated by the competition between the two higher-order singularities. This results in the presence of special loci along which the dynamics is identical \textit{at all} length and time scales.