• Corpus ID: 201106529

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}
}
  • Pax Kivimae
  • Published 20 August 2019
  • Physics
  • arXiv: Probability
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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