• Corpus ID: 236950688

Fluctuations of the free energy of the mixed $p$-spin mean field spin glass model

@inproceedings{Banerjee2021FluctuationsOT,
  title={Fluctuations of the free energy of the mixed \$p\$-spin mean field spin glass model},
  author={Debapratim Banerjee and David Belius},
  year={2021}
}
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; Tal10; Tal11; Pan13b]. An important step in the solution of the model is the computation of the free energy. The Parisi formula [Par80; Par79; Gue03; Tal06; Pan13a] gives the typical value of the free energy in the form of a law of large numbers. This article studies the fluctuations of free energy… 
Fluctuations of the free energy in p-spin SK models on two scales
A BSTRACT . 20 years ago, Bovier, Kurkova, and L¨owe [5] proved a central limit theorem (CLT) for the fluctuations of the free energy in the p -spin version of the Sherrington-Kirkpatrick model of
Mean Field Spin Glass Models under Weak External Field
. 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

References

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We consider the random fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model in the high temperature regime. Using the martingale approach of Comets and Neveu as
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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 $\beta = 1 +\alpha \sqrt{ \log(N) } N^{-1/3}$.
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We consider a spin system containing pure two spin Sherrington–Kirkpatrick Hamiltonian with Curie–Weiss interaction. The model where the spins are spherically symmetric was considered by Baik and Lee
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We consider the fluctuations of the free energy for the 2-spin spherical Sherrington–Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian
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In this chapter we prove the Parisi formula, which gives the limiting value of the free energy per site for the Sherrington-Kirkpatrick model at each temperature, starting with the famous result of
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