# Fluctuations of the free energy in the mixed p-spin models with external field

@article{Chen2015FluctuationsOT, title={Fluctuations of the free energy in the mixed p-spin models with external field}, author={Wei-Kuo Chen and Partha S. Dey and Dmitry Panchenko}, journal={Probability Theory and Related Fields}, year={2015}, volume={168}, pages={41-53} }

We show that the free energy in the mixed p-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincaré inequality. This complements the result of Chatterjee who showed that the free energy superconcentrates when there is no external field. For models without odd p-spin interactions for $$p\geqslant 3$$p⩾3, we prove the central limit theorem for the free energy at any temperature and give an…

## 17 Citations

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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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