Scaling and universality in glass transition.

Antonio De Candia,Antonio Coniglio,Annalisa Fierro

doi:10.1038/srep26481

Antonio De Candia, Antonio Coniglio + Show 1 more

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https://doi.org/10.1038/srep26481

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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 〈q2(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 dc = 8.

Highlights

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
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 dc = 8
Generalizing the cluster approach considered for the continuous dynamic transition[5,6], we are able to predict the dynamical behavior for the correlator and for the dynamical susceptibility of the Fredrickson and Andersen (FA) facilitated model, including universal scaling laws that relate dynamical exponents with the static universal exponents of bootstrap percolation (BP)

Summary

Introduction

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. 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 dc = 8. These new predictions are verified numerically on both FA facilitated model and MCT model B All these results suggest a general common mechanism for discontinuous glass transition at mean field level, based on a static transition in the same universality class of bootstrap percolation with a diverging static length, which is responsible for the origin of scaling and universality present in such a wide range of systems, apparently very different from each other. Given a two step relaxation, the correlator can be written as Φ(t) − mc β eter BP exponent, τβ ∼

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