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

TL;DR

This paper extends replica liquid theory to binary mixtures with large size disparities, predicting multiple glass phases and complex energy landscapes using two-step replica symmetry breaking in the mean-field limit.

Contribution

It introduces a novel theoretical framework incorporating 2RSB to describe multiple glass transitions in binary mixtures with large size disparities.

Findings

Identification of three distinct glass phases: 1RSB double glass, 1RSB single glass, and 2RSB double glass.

Prediction of a critical size ratio beyond which multiple glass phases emerge.

Characterization of the energy landscape differences among the glass phases.

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.