Multiple glass singularities and isodynamics in a core-softened model for glass-forming systems

We investigate the slow dynamics of a simple glass former whose interaction potential is the sum of a hard core and a square shoulder repulsion. According to mode coupling theory, the competition between the two repulsive length scales gives rise to a complex dynamic scenario: besides the fluid-glass line, the theory predicts a glass-glass line in the temperature-packing fraction plane with two end points. Interestingly, for critical values of the square-shoulder parameters, such end points can be accessed from the liquid phase. We verify, via extensive numerical simulations, the existence of both points through the observation of an unconventional subdiffusive/logarithmic dynamical behavior. Unexpectedly, we also discover that the simultaneous presence of two end points generates special loci in the state diagram along which the dynamics is identical at all length and time scales.