SciPost Submission Page

Stationarization and Multithermalization in spin glasses

by Pierluigi Contucci, Federico Corberi, Jorge Kurchan, Emanuele Mingione

Submission summary

As Contributors: Federico Corberi · Emanuele Mingione
Arxiv Link: (pdf)
Date accepted: 2021-05-10
Date submitted: 2021-04-06 15:06
Submitted by: Mingione, Emanuele
Submitted to: SciPost Physics
Academic field: Physics
  • Mathematical Physics
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


We develop further the study of a system in contact with a multibath having different temperatures at widely separated timescales. We consider those systems that do not thermalize in finite times when in contact with an ordinary bath but may do so in contact with a multibath. Thermodynamic integration is possible, thus allowing one to recover the stationary distribution on the basis of measurements performed in a `multi-reversible' transformation. We show that following such a protocol the system is at each step described by a generalization of the Boltzmann-Gibbs distribution, that has been studied in the past. Guerra's bound interpolation scheme for spin-glasses is closely related to this: by translating it into a dynamical setting, we show how it may actually be implemented in practice. The phase diagram plane of temperature vs "number of replicas", long studied in spin-glasses, in our approach becomes simply that of the two temperatures the system is in contact with. We suggest that this representation may be used to directly compare phenomenological and mean-field inspired models.Finally, we show how an approximate out of equilibrium probability distribution may be inferred experimentally on the basis of measurements along an almost reversible transformation.

Published as SciPost Phys. 10, 113 (2021)

Reports on this Submission

Anonymous Report 1 on 2021-4-28 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2012.03922v2, delivered 2021-04-28, doi: 10.21468/SciPost.Report.2850


The resubmitted papers presents marginal modifications address the points I raised. A short and not very informative introduction (comprising 9 lines and a summary of the content of the sections), and a few sentences have been added. The only criticism they addressed in a satisfactory way was to give a professional description of their simulations (though probably the authors did not simulate systems of 10^12 spins as they claim). In deciding for this minimalistic strategy rather than going through a deep revision as I suggested the authors have probably lost an occasion to make their work appreciable by a wider community. I do not oppose myself to the publications.

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