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Arrangement of nearby minima and saddles in the mixed spherical energy landscapes
by Jaron Kent-Dobias
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Jaron Kent-Dobias |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2306.12779v3 (pdf) |
| Date accepted: | 2023-12-13 |
| Date submitted: | 2023-12-05 08:42 |
| Submitted by: | Kent-Dobias, Jaron |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The mixed spherical models were recently found to violate long-held assumptions about mean-field glassy dynamics. In particular, the threshold energy, where most stationary points are marginal and that in the simpler pure models attracts long-time dynamics, seems to lose significance. Here, we compute the typical distribution of stationary points relative to each other in mixed models with a replica symmetric complexity. We examine the stability of nearby points, accounting for the presence of an isolated eigenvalue in their spectrum due to their proximity. Despite finding rich structure not present in the pure models, we find nothing that distinguishes the points that do attract the dynamics. Instead, we find new geometric significance of the old threshold energy, and invalidate pictures of the arrangement of most marginal inherent states into a continuous manifold.
Author comments upon resubmission
List of changes
It is difficult to list each specific change because of the nature of the suggested amendments. Here is a point-by-point summary of what we did:
- Large portions of the calculations for the two-point complexity, the isolated eigenvalue, and the entirety of the Franz–Parisi potential were moved into appendices.
- The explanation of steps in these calculations was expanded, especially in the calculation of the complexity.
- Much of the text was edited for clarity, with confusing statements amended or removed (including but not limited to those flagged by the referees).
- A new subsection 3.2 was added to the results section briefly detailing the mutual geometry of saddle points implied by the two-point complexity.
- More motivation has been given for our interest in specific results, including several expectations of what might be learned from the two-point complexity that were not borne out.
- More references were added where appropriate.
Published as SciPost Phys. 16, 001 (2024)