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Annealed averages in spin and matrix models
by Laura Foini, Jorge Kurchan
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|Authors (as Contributors):||Laura Foini|
|Arxiv Link:||https://arxiv.org/abs/2104.04363v3 (pdf)|
|Date submitted:||2021-10-26 14:07|
|Submitted by:||Foini, Laura|
|Submitted to:||SciPost Physics|
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.
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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.