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

@article{Baik2016FluctuationsOT, title={Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model with Ferromagnetic Interaction}, author={Jinho Baik and Ji Oon Lee}, journal={Annales Henri Poincar{\'e}}, year={2016}, volume={18}, pages={1867-1917} }

We consider a spherical spin system with pure 2-spin spherical Sherrington–Kirkpatrick Hamiltonian with ferromagnetic Curie–Weiss interaction. The system shows a two-dimensional phase transition with respect to the temperature and the coupling constant. We compute the limiting distributions of the free energy for all parameters away from the critical values. The zero temperature case corresponds to the well-known phase transition of the largest eigenvalue of a rank 1 spiked random symmetric…

## 33 Citations

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### Free energy of bipartite spherical Sherrington–Kirkpatrick model

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We consider the free energy of the bipartite spherical Sherrington--Kirkpatrick model. We find the critical temperature and prove the limiting free energy for all non-critical temperature. We also…

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We prove the existence of a critical regime of fluctuation of the ground-state energy of the spherical Sherrington-Kirkpatrick model in an external field. Such regime was conjectured in [2,12], and…

### Fluctuation of the Free Energy of Sherrington–Kirkpatrick Model with Curie–Weiss Interaction: The Paramagnetic Regime

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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 describe the fluctuations of the overlap between two replicas in the 2-spin spherical SK model about its limiting value in the low temperature phase. We show that the fluctuations are of order…

### Free energy fluctuations of the two-spin spherical SK model at critical temperature

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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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### Central limit theorem near the critical temperature for the overlap in the 2-spin spherical SK model

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We prove a central limit theorem for the normalized overlap between two replicas in the spherical SK model in the high temperature phase. The convergence holds almost surely with respect to the…

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