title: Hopping and the Stokes-Einstein relation breakdown in simple glass formers.
abstract: One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.
authors.affiliation: Departments of Chemistry and Physics, Duke University, Durham, NC 27708;
authors.forename: Patrick
authors.initials: P
authors.lastname: Charbonneau
authors.affiliation: Departments of Chemistry and Dipartimento di Fisica, Sapienza Università di Roma, I-00185 Rome, Italy; jinyuliang@gmail.com giorgio.parisi@roma1.infn.it.
authors.forename: Yuliang
authors.initials: Y
authors.lastname: Jin
authors.affiliation: Dipartimento di Fisica, Sapienza Università di Roma, I-00185 Rome, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, Istituto per i Processi Chimico Fisici, Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy; and jinyuliang@gmail.com giorgio.parisi@roma1.infn.it.
authors.forename: Giorgio
authors.initials: G
authors.lastname: Parisi
authors.affiliation: Laboratoire de Physique Théorique, Ecole Normale Supérieure, UMR 8549 CNRS, 75005 Paris, France.
authors.forename: Francesco
authors.initials: F
authors.lastname: Zamponi
keywords: activated processes; cavity method; random first-order transition