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

@article{Baik2015FluctuationsOT,
  title={Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model},
  author={Jinho Baik and Ji Oon Lee},
  journal={Journal of Statistical Physics},
  year={2015},
  volume={165},
  pages={185-224}
}
  • J. Baik, J. Lee
  • Published 27 May 2015
  • Physics
  • Journal of Statistical Physics
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. 
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References

SHOWING 1-10 OF 60 REFERENCES
The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case
We study the fluctuations of free energy, energy and entropy in the high temperature regime for the Sherrington-Kirkpatrick model of spin glasses. We introduce here a new dynamical method with the
Some rigorous results on the Sherrington-Kirkpatrick spin glass model
We prove that in the high temperature regime (T/J>1) the deviation of the total free energy of the Sherrington-Kirkpatrick (S-K) spin glass model from the easily computed log Av(Z N ({βJ}))
Some comments on the Sherrington-Kirkpatrick model of spin glasses
In this paper the high-temperature phase of general mean-field spin glass models, including the Sherrington-Kirkpatrick (SK) model, is analyzed. The free energy in zero magnetic field is calculated
Large deviations in the free energy of mean-field spin glasses.
TLDR
The exponentially small probability of finding a system with intensive free energy smaller than the most likely one is computed by computing the average value of the partition function to the power n as a function of n.
Universality in Sherrington–Kirkpatrick's spin glass model
The sphericalp-spin interaction spin glass model: the statics
The static properties of the sphericalp-spin interaction spin glass model are calculated using the replica method. It is shown that within the Parisi scheme the most general solution is the one-step
The Thermodynamic Limit in Mean Field Spin Glass Models
Abstract: We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as
Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
Abstract: By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick
Large deviations in spin-glass ground-state energies
Abstract.The ground-state energy E0 of a spin glass is an example of an extreme statistic. We consider the large deviations of this energy for a variety of models when the number of spins N goes to
The parisi formula
In this chapter we prove the Parisi formula, which gives the limiting value of the free energy per site for the Sherrington-Kirkpatrick model at each temperature, starting with the famous result of
...
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