SciPost logo

SciPost Submission Page

Annealed averages in spin and matrix models

by Laura Foini, Jorge Kurchan

This is not the latest submitted version.

This Submission thread is now published as

Submission summary

Authors (as Contributors): Laura Foini
Submission information
Arxiv Link: https://arxiv.org/abs/2104.04363v3 (pdf)
Date submitted: 2021-10-26 14:07
Submitted by: Foini, Laura
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Statistical and Soft Matter Physics
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.

Current status:
Has been resubmitted


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.


Reports on this Submission

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

Report

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

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Login to report


Comments

Anonymous on 2021-11-29  [id 1984]

Category:
remark

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.