Long-wavelength fluctuations lead to a model of the glass crossover

Abstract

PACS 64.70.Q--Theory and modeling of glass transitions Abstract -The effect of long wavelength fluctuations on the Mode-Coupling-Theory (MCT) dynamical singularity at Tc in the β regime is studied by means of the standard field-theoretical procedure for a genuine second-order phase transition. The resulting perturbative loop expansion can be resummed leading to an extension of the MCT equation for the critical correlator with local random fluctuations of the separation parameter. The corresponding model explains both qualitatively and quantitatively why the MCT dynamical singularity is transformed into a crossover from relaxational to activated dynamics. Dynamical Heterogeneities emerge naturally as the ergodicity-restoring mechanism instead of ad hoc hopping processes.

The glass crossover from mean-field Spin-Glasses to supercooled liquids

“…Indeed as discussed in [2] within SBR the unphysical singularity predicted by MCT is avoided and replaced by a dynamical crossover from relaxational to activated-like dynamics. Further study of the SBR equations is unvealing a rich phenomenology and a rather non-trivial characterization of the qualitative and quantitative changes occurring at the glass crossover [3,4].…”

“…In a few words the calculation shows that there is an equivalence between a dynamical effective theory a la Landau (called glassy critical theory (GCT) below) on one side and SBR on the other side. The explanation of this connection was sketched in [2] in a way accessible for people familiar with statistical field theory and the field theoretical approach to critical phenomena. While the actual derivation is rather technical and still unpublished, one does not need to master all the technical details in order to understand it physically.…”

“…In order to make progress we should work with an object that we expect to be well-defined also in a finite-system size. This can be done by going back to our original dynamical problem [2]. Indeed we expect that if we consider the dynamical expansion (6) over an appropriate large but not infinite time-scale it makes sense to assume that even in a finite-size system the correlator will stay close to the plateau value.…”

“…We have to be close to the critical temperature |τ | ≪ 1 and consider a large but not infinite time scale τ β ∝ 1/|τ | 1/(2a) in order to see that C 0 (t) remains close to the plateau both above and below T c . The technical details of this analysis [2] are largely unpublished but the result boils down to the following scaling forms for the leading order term:…”

“…Stochastic-Beta-Relaxation (SBR) is model of the glass crossover that I have introduced in a recent publication [2]. The model describes the time evolution of the density-density correlator of the liquid in the β-regime, i.e.…”