# Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model

@article{Baik2015FluctuationsOT, title={Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model}, author={Jinho Baik and Ji Oon Lee}, journal={Journal of Statistical Physics}, year={2015}, volume={165}, pages={185-224} }

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 distribution when the temperature is above the critical temperature, and to the GOE Tracy–Widom distribution when the temperature is below the critical temperature. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved.

## 48 Citations

Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model with Ferromagnetic Interaction

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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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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;…

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