2014/02/27 by Jeferson J. Arenzon, Antonio Coniglio, Annalisa Fierro +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Continuum percolation theory #Critical dimension #Critical exponent #Directed percolation #Ergodicity #Geometry #Glass transition #Lattice (music) #Liquid Crystal Research Advancements #Material Dynamics and Properties #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Physics #Quantum mechanics #Relaxation (psychology) #Scaling #Spin glass #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.90.020301
published as Phys. Rev. E 90, 020301 (2014)
arxiv created 2014/02/27 · openalex publication_date 2014/08/26 · arxiv updated 2014/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At the mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows one to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the F(12) schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields predictions for dynamic relaxation exponents below an upper critical dimension of 6.