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}
}
  • J. Baik, J. Lee
  • Published 5 July 2016
  • Mathematics, Physics
  • Annales Henri Poincaré
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… 

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