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Annealed averages in spin and matrix models

by Laura Foini, Jorge Kurchan

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Authors (as registered SciPost users): Laura Foini
Submission information
Preprint Link:  (pdf)
Date submitted: 2021-10-26 14:07
Submitted by: Foini, Laura
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


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.

List of changes

In the revised version we have improved the presentation of our work following the remarks of the referees. A detailed list of changes can be found in the letters in reply to the referees.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 1 on 2021-10-26 (Invited Report)


The authors have replied to the points made by myself and the other referee thoroughly and the revised version is suitable for publication.

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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.