SciPost Submission Page
Theory of Kinetically-Constrained-Models Dynamics
by Gianmarco Perrupato, Tommaso Rizzo
Submission summary
| Authors (as registered SciPost users): | Gianmarco Perrupato |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00008v1 (pdf) |
| Date submitted: | 2024-09-09 20:04 |
| Submitted by: | Perrupato, Gianmarco |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic dynamical equations equal to those of Mode-Coupling-Theory. Analytical predictions obtained for the dynamical exponents are successfully compared with numerical simulations in a wide range of models, including the case of generic values of the connectivity and the facilitation, random pinning and fluctuating facilitation. The theory is thus validated for both continuous and discontinuous transitions and also in the case of higher order critical points characterized by logarithmic decays.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1. Studies the dynamics of a class of kinetically constrained models (f-spin facilitated Fredrikson-Andersen models, part of a family of KCMs which are very relevant for understanding glasses).
2. By placing the models in a z-tree (rather than on a lattice with loops) the problem becomes effectively mean field, and therefore amenable to a technique like mode-coupling theory (and specifically schematic MCT in this case).
3. The paper obtains the MCT exponents exactly, thus completing the MCT study of such Bethe-lattice KCMs.
4. The main result is that of eq.18/19, with table 1 giving the exponent as a function of f and z.
Weaknesses
The paper delivers what it purports to do, so in that sense I cannot see any weaknesses. It is written in a way that will be accessible to experts in this field (especially those like me that have been around it since the time MCT was more fashionable).
Report
This paper studies the dynamics of a class of kinetically constrained models (f-spin facilitated Fredrikson-Andersen models). These are part of a family of KCMs which are very relevant for understanding glasses (cf. East model or constrained lattice gases). In an f-FA model a spin can flip if f of its neighbours are in a specific state (say up), this kinetic constraint leading to slow relaxation when that state is scarce (e.g. at low T when there are few of the energetically expensive ups). KCMs in low dimensional square lattices, and with low f (like the FA or East models) behave in a very non mean-field way. Interestingly, when place in mean-field like geometries, such as a Cayley tree, they can display mean-field like dynamics, in particular for larger f (when the KCM is more constrained) when the KCM has an ergodicity breaking singularity as some finite average density of facilitating sites (i.e. finite temperatures).
Early work had shown schematic MCT like behaviour of KCMs in trees, but this programme of work was not completed. This is what this paper mostly does. Specifically, by considering the persistence function (which is an alternative to the autocorrelation function to quantify relaxation, and often simpler to study) the paper finds the MCT exponents of f-FA in z-trees exactly, thus completing the MCT study of such Bethe-lattice KCMs. The main result is that of eq.18/19, with table 1 giving the exponent as a function of f and z. There are more results, like doing the same in the case of random pinning (which is known in other mean-field systems to lead to a higher order MCT singularity), and they also argue on convincing grounds that their results for the persistence also capture the behavior of the autocorrelator in this kind of geometries.
The paper is easy to follow for those familiar with MCT methods. The main text deals with the essential aspects of the approach that leads to the central results, with other technical details relegated to the appendices. Overall this is a solid piece of work that fills gaps in the mean-field study of KCMs. I recommend publication as is.
Recommendation
Publish (meets expectations and criteria for this Journal)