Ideal glass-glass transitions and logarithmic decay of correlations in a simple system

We calculate the ideal-glass-transition line for adhesive hard spheres in the temperature-volume-fraction plane within the framework of the mode-coupling theory. We find two intersecting lines, controlled by the hard-core and the adhesive parts of the potential respectively, giving rise to two different mechanisms for structural arrest. In the glass region we identify the presence of a glass-glass-transition line ending in a cusp bifurcation which causes, even in the nearby liquid region, a logarithmic decay of correlations.