Order of fluctuations of the free energy in the SK model at critical temperature

Wei Kuo Chen, Wai Kit Lam

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We present an elementary approach to the order of fluctuations for the free energy in the Sherrington-Kirkpatrick mean field spin glass model at and near the critical temperature. It is proved that at the critical temperature the variance of the free energy is of O((logN)2): In addition, we show that if one approaches the critical temperature from the low temperature regime at the rate O(N) for some α > 0; then the variance is of O((logN)2 + N1-α).

Original languageEnglish (US)
Pages (from-to)809-816
Number of pages8
Issue number1
StatePublished - 2019

Bibliographical note

Funding Information:
Both authors thank Sourav Chatterjee for explaining Talagrand’s upper bound for the variance of the free energy at the critical temperature and Erik Bates for the illuminating discussion and careful reading. They also thank the anonymous referee for providing many useful suggestions regarding the presentation of the paper. The first author’s research is partially supported by NSF grants DMS-17-52184.

Publisher Copyright:
© 2019 ALEA, Lat. Am. J. Probab. Math. Stat.


  • Disorder chaos
  • Sherrington-Kirkpatrick model
  • Spin glass


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