Patch-repetition correlation length in glassy systems

Institut de Physique Théorique (IPhT), CEA, and CNRS URA 2306 - F-91191 Gif-sur-Yvette, France, EU

Received: 16 January 2012
Accepted: 11 April 2012

Abstract

We obtain the patch-repetition entropy Σ within the Random First-Order Transition (RFOT) theory 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, Σ(ℓ), scales as s_cℓ^d+Aℓ^{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. As a consequence, the only meaningful length that can be defined from patch-repetition is the crossover length ξ=A/s_c. We relate ξ 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, into 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.