  Building on mode-coupling-theory calculations, we report a novel scenario for
multiple glass transitions in a purely repulsive spherical potential: the
square-shoulder. The liquid-glass transition lines exhibit both melting by
cooling and melting by compression as well as associated diffusion anomalies,
similar to the ones observed in water. Differently from all previously
investigated models, here for small shoulder widths a glass-glass line is found
that is disconnected from the liquid phase. Upon increasing the shoulder width
such a glass-glass line merges with the liquid-glass transition lines,
featuring two distinct endpoint singularities that give rise to logarithmic
decays in the dynamics. These findings can be explained analytically by the
interplay of different repulsive length scales.

Statistical Mechanics