# Critical Fluctuations for the Spherical Sherrington-Kirkpatrick Model in an External Field

@article{Kivimae2019CriticalFF, title={Critical Fluctuations for the Spherical Sherrington-Kirkpatrick Model in an External Field}, author={Pax Kivimae}, journal={arXiv: Probability}, year={2019} }

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 occurs with external field strength $h=O(N^{-1/6})$. Additional results are proven for $\beta$-analogues of the spherical Sherrington-Kirkpatrick model, and models with a Curie-Weiss term. In particular, we introduce a three-parameter family $TW_{\beta,w}^h$ (generalizing the two-parameter family of…

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