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

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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 matrix. As an intermediate step, we establish a central limit theorem for the linear statistics of rank 1 spiked random symmetric matrices.
Publisher
SPRINGER BASEL AG
Issue Date
2017-06
Language
English
Article Type
Article
Citation

ANNALES HENRI POINCARE, v.18, no.6, pp.1867 - 1917

ISSN
1424-0637
DOI
10.1007/s00023-017-0562-5
URI
http://hdl.handle.net/10203/224049
Appears in Collection
MA-Journal Papers(저널논문)
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