Patch-repetition correlation length in glassy systems

Abstract

We obtain the patch-repetition entropy Sigma within the Random First Order Transition theory (RFOT) and for the square plaquette system, a model related to the dynamical facilitation theory of glassy dynamics. We find that in both cases the entropy of patches of linear size l, Sigma(l), scales as s_c l^d+A l^{d-1} down to length-scales of the order of one, where A is a positive constant, s_c is the configurational entropy density and d the spatial dimension. In consequence, the only meaningful length that can be defined from patch-repetition is the cross-over length xi=A/s_c. We relate xi to the typical length-scales already discussed in the literature and show that it is always of the order of the largest static length. Our results provide new insights, which are particularly relevant for RFOT theory, on the possible real space structure of super-cooled liquids. They suggest that this structure differs from a mosaic of different patches having roughly the same size.

6 pages

References in corpus (6)

• Rigorous Inequalities between Length and Time Scales in Glassy Systems
• Analytic determination of dynamical and mosaic length scales in a Kac glass model
• Caging and mosaic lengthscales in plaquette spin models of glasses
• Characterizing order in amorphous systems
• Random pinning in glassy spin models with plaquette interactions
• Aging and relaxation near Random Pinning Glass Transitions

Cited by in corpus (20)

• The role of local structure in dynamical arrest
• Perspective: The Glass Transition
• Identification of long-lived clusters and their link to slow dynamics in a model glass former
• Information-theoretic measurements of coupling between structure and dynamics in glass-formers
• Lifetimes and Lengthscales of Structural Motifs in a Model Glassformer
• Theory of the Structural Glass Transition: A Pedagogical Review
• The race to the bottom: approaching the ideal glass?
• Non-Equilibrium Phase Transition in an Atomistic Glassformer: the Connection to Thermodynamics
• Phase transition for quenched coupled replicas in a plaquette spin model of glasses
• Locally favoured structures and dynamic length scales in a simple glass-former
• The nature of geometric frustration in the Kob-Andersen mixture
• The melting of stable glasses is governed by nucleation-and-growth dynamics
• Static correlations functions and domain walls in glass-forming liquids: the case of a sandwich geometry
• Investigating amorphous order in stable glasses by random pinning
• Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids
• Emergence of cooperatively reorganizing cluster and super-Arrhenius dynamics of fragile supercooled liquids
• Counting metastable states in a kinetically constrained model using a patch repetition analysis
• Yielding of a Model Glassformer: an Interpretation with an Effective System of Icosahedra
• How non-equilibrium correlations in active matter reveal the topological crossover in glasses
• Static self-induced heterogeneity in glass-forming liquids: Overlap as a microscope