2008/04/08 by Edan Lerner, Itamar Procaccia · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Binary number #Fragility #Function (biology) #Glass properties and applications #Material Dynamics and Properties #Mathematics #Physics #Relaxation (psychology) #Simple (philosophy) #Statistical mechanics #Statistical physics #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.78.020501
4 pages, 5 figures
arxiv created 2008/04/08 · openalex publication_date 2008/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally favored regions (clusters) that are long-lived but each of which relaxes as a simple function of time. Without the clusters, the relaxation of the background is simply determined by one typical length, which we deduce from an elementary statistical mechanical argument. The total relaxation function (which depends on time in a nontrivial manner) is quantitatively determined as a weighted sum over the clusters and the background. The "fragility" in this system can be understood quantitatively since it is determined by the temperature dependence of the number fractions of the locally favored regions.