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We calculate the ideal-glass-transition line for adhesive hard spheres in thetemperature-volume-fraction plane within the framework of the mode-couplingtheory. We find two intersecting lines, controlled by the hard-core and theadhesive part of the potential respectively, giving rise to two differentmechanisms for structural arrest. In the glass region we identify the presenceof a glass-glass-transition line ending in a cusp bifurcation which causes,even in the close by liquid region, a logarithmic decay of correlations

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