SciPost Submission Page
Theory of Kinetically-Constrained-Models Dynamics
by Gianmarco Perrupato, Tommaso Rizzo
Submission summary
| Authors (as registered SciPost users): | Gianmarco Perrupato · Tommaso Rizzo |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00008v2 (pdf) |
| Date submitted: | 2024-11-15 18:45 |
| Submitted by: | Perrupato, Gianmarco |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| 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
List of changes
1) In order to make the introduction more complete, we decided to incorporate Section 2.1 into it. In the new version of the manuscript we discuss the derivation of the dynamical equation in section 2, we discuss the variations of the Fredrickson-Andersen model (FAM) in section 3, and we present the connection between persistence and correlation in section 4
2) we extended the discussion about Phys Rev E 110, 044312 (2024) in section 4. In particular we added a new figure (figure 7) to give an example of correlations induced by the presence of permanently blocked spins
3) We extended the conclusions with a comment regarding the connection between statics and dynamics