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

Abstract: 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 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 new glass phase called the 2RSB double glass where both components vitrify simultaneously but with an energy landscape topography distinct from the 1RSB double glass.