• Corpus ID: 221969933

Fluctuations of the 2-spin SSK model with magnetic field

  title={Fluctuations of the 2-spin SSK model with magnetic field},
  author={Benjamin Landon and Philippe Sosoe},
  journal={arXiv: Probability},
We analyze the fluctuations of the free energy, replica overlaps, and overlap with the magnetic fields in the quadratic spherial SK model with a vanishing magnetic field. We identify several different behaviors for these quantities depending on the size of the magnetic field, confirming predictions by Fyodorov-Le Doussal and recent work of Baik, Collins-Wildman, Le Doussal and Wu. 
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Free energy fluctuations of the two-spin spherical SK model at critical temperature
  • B. Landon
  • Mathematics
    Journal of Mathematical Physics
  • 2022
The fluctuations of the free energy of the $2-spin spherical Sherrington-Kirkpatrick model at critical temperature are investigated and it is proved the existence of a critical window on the scale of $\beta = 1 +\alpha \sqrt{ \log(N) } N^{-1/3}$.
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