Fluctuations of the Free Energy of the Spherical Sherrington-Kirkpatrick Model

We consider the fluctuations of the free energy for the 2-spin spherical Sherrington-Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian distribution when the temperature is above the critical temperature, and to the GOE Tracy-Widom distribution when the temperature is below the critical temperature. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved
Publisher
SPRINGER
Issue Date
2016-10
Language
ENG
Keywords

SPIN-GLASS MODEL; SAMPLE COVARIANCE MATRICES; INTERMEDIATE DISORDER REGIME; LOCAL EIGENVALUE STATISTICS; LINEAR SPECTRAL STATISTICS; DIRECTED POLYMERS; WIGNER MATRICES; RANDOM ENVIRONMENT; BETA-ENSEMBLES; UNIVERSALITY

Citation

JOURNAL OF STATISTICAL PHYSICS, v.165, no.2, pp.185 - 224

ISSN
0022-4715
DOI
10.1007/s10955-016-1610-0
URI
http://hdl.handle.net/10203/214103
Appears in Collection
MA-Journal Papers(저널논문)
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