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

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