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Annealed averages in spin and matrix models
by Laura Foini, Jorge Kurchan
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Laura Foini |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2104.04363v3 (pdf) |
| Date submitted: | Oct. 26, 2021, 2:07 p.m. |
| Submitted by: | Laura Foini |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
A disordered system is denominated 'annealed' when the interactions themselves may evolve and adjust their values to lower the free energy. The opposite ('quenched') situation when disorder is fixed, is the one relevant for physical spin-glasses, and has received vastly more attention. Other problems however are more natural in the annealed situation: in this work we discuss examples where annealed averages are interesting, in the context of matrix models. We first discuss how in practice, when system and disorder adapt together, annealed systems develop 'planted' solutions spontaneously, as the ones found in the study of inference problems. In the second part, we study the probability distribution of elements of a matrix derived from a rotationally invariant (not necessarily Gaussian) ensemble, a problem that maps into the annealed average of a spin glass model.
Anonymous on 2021-11-29 [id 1984]
I am satisfied with the authors' response to my previous report. I would only like them to add at least one reference to papers where the conditions for validity of steepest descent in integrals where the dimensionality scales proportional to the large parameter in the exponent are discussed. The authors agree in their reply that this point is nontrivial and refer to literature on that topic, but without given pointers for the reader to that literature.