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Annealed averages in spin and matrix models

by Laura Foini, Jorge Kurchan

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Submission summary

As Contributors: Laura Foini
Arxiv Link: (pdf)
Date accepted: 2022-01-26
Date submitted: 2021-12-09 12:45
Submitted by: Foini, Laura
Submitted to: SciPost Physics
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.

Published as SciPost Phys. 12, 080 (2022)

List of changes

We have made a small modification to the text in order to reply to the referee question (see the reply to the comment)

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