Multiple glass transitions and higher-order replica symmetry breaking of binary mixtures

We extend the replica liquid theory in order to describe multiple glass transitions of binary mixtures with large size disparities, by taking into account two-step symmetry breaking (2RSB). determine phase diagram mixture and small particles large-dimension limit where mean-field becomes exact. When ratio is beyond a critical value, predicts three distinct phases; (i) 1RSB double both components vitrify simultaneously, (ii) single only are frozen while remain mobile, (iii) new called 2RSB simultaneously but an energy landscape topography from glass.