Scaling and universality in glass transition

Abstract

Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field theory, for such systems by considering the behavior of the density correlator <q(t)> and the dynamical susceptibility <q^2(t)> -<q(t)>^2. Focusing on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe lattice, we extend a cluster approach that was previously developed for continuous glass transitions by Arenzon et al (Phys. Rev. E 90, 020301(R) (2014)) to describe the decay to the plateau, and consider a damage spreading mechanism to describe the departure from the plateau. We predict scaling laws, which relate dynamical exponents to the static exponents of mean field bootstrap percolation. The dynamical behavior and the scaling laws for both density correlator and dynamical susceptibility coincide with those predicted by MCT. These results explain the origin of scaling laws and the universal behavior associated with the glass transition in mean field, which is characterized by the divergence of the static length of the bootstrap percolation model with an upper critical dimension d_c=8.

16 pages, 9 figures

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• Mean field theory of the swap Monte Carlo algorithm
• Solvable Models of Supercooled Liquids in Three Dimensions
• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Fractal fluctuations at mixed-order transitions in interdependent networks
• The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions
• A small-world search for quantum speedup: How small-world interactions can lead to improved quantum annealer designs
• Universal behaviour of the glass and the jamming transitions in finite dimensions
• Temperature dependence of the transition packing fraction of thermal jamming in a harmonic soft sphere system
• Cluster structure and dynamics in gels and glasses
• Universal behavior of the apparent fragility in ultraslow glass forming systems
• Theory of Kinetically-Constrained-Models Dynamics