• Corpus ID: 221969933

Fluctuations of the 2-spin SSK model with magnetic field

@article{Landon2020FluctuationsOT,
  title={Fluctuations of the 2-spin SSK model with magnetic field},
  author={Benjamin Landon and Philippe Sosoe},
  journal={arXiv: Probability},
  year={2020}
}
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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8 Citations
Highly Influential Citations
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Background Citations
2
Methods Citations
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Results Citations
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8 Citations

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Citation Type

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The Sherrington-Kirkpatrick [SK75] model and its variants [Der80; GM84; Tal00] are important models of disordered magnetic systems and paradigmatic examples in the theory of complex systems [MPV87;…
Free energy fluctuations of the two-spin spherical SK model at critical temperature
  • B. Landon
  • Mathematics
    Journal of Mathematical Physics
  • 2022
TLDR
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 $\beta = 1 +\alpha \sqrt{ \log(N) } N^{-1/3}$.
Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington–Kirkpatrick model
We revisit the gradient descent dynamics of the spherical Sherrington–Kirkpatrick (p = 2) model with finite number of degrees of freedom. For fully random initial conditions we confirm that the…
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. We study the fluctuation and limiting distribution of free energy in mean-field Ising spin glass models under weak external fields. We prove that at high temperature, there are three sub-regimes…
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Optimization landscape in the simplest constrained random least-square problem
TLDR
The compatibility threshold α c < 1 is found which is the value of α beyond which a large random linear system on the N-sphere becomes typically incompatible.

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