# Free energy fluctuations of the two-spin spherical SK model at critical temperature

@article{Landon2022FreeEF,
title={Free energy fluctuations of the two-spin spherical SK model at critical temperature},
author={Benjamin Landon},
journal={Journal of Mathematical Physics},
year={2022}
}
• B. Landon
• Published 13 October 2020
• Mathematics
• Journal of Mathematical Physics
We investigate the fluctuations of the free energy of the two-spin spherical Sherrington–Kirkpatrick model at critical temperature β c = 1. When β = 1, we find asymptotic Gaussian fluctuations with variance [Formula: see text], confirming in the spherical case a physics prediction for the SK model with Ising spins. We, furthermore, prove the existence of a critical window on the scale [Formula: see text]. For any [Formula: see text], we show that the fluctuations are at most order [Formula: see…
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## References

SHOWING 1-10 OF 45 REFERENCES
Order of fluctuations of the free energy in the SK model at critical temperature
• Physics
Latin American Journal of Probability and Mathematical Statistics
• 2019
We present an elementary approach to the order of fluctuations for the free energy in the Sherrington-Kirkpatrick mean field spin glass model at and near the critical temperature. It is proved that
Disorder chaos and multiple valleys in spin glasses
We prove that the Sherrington-Kirkpatrick model of spin glasses is chaotic under small perturbations of the couplings at any temperature in the absence of an external field. The result is proved for
Fluctuations of the overlap at low temperature in the 2-spin spherical SK model
• Mathematics
• 2019
We describe the fluctuations of the overlap between two replicas in the 2-spin spherical SK model about its limiting value in the low temperature phase. We show that the fluctuations are of order
Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model with Ferromagnetic Interaction
• Mathematics, Physics
• 2016
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
Spherical Spin Glass Model with External Field
• Physics
• 2020
We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model
Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model
• Physics
• 2015
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
Large deviations in the free energy of mean-field spin glasses.
• Physics, Mathematics
Physical review letters
• 2008
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.
Random Matrices and Complexity of Spin Glasses
• Computer Science
• 2010
This study enables detailed information about the bottom of the energy landscape, including the absolute minimum, and the other local minima, and describes an interesting layered structure of the low critical values for the Hamiltonians of these models.
Free energy of bipartite spherical Sherrington–Kirkpatrick model
• Physics
• 2017
We consider the free energy of the bipartite spherical Sherrington--Kirkpatrick model. We find the critical temperature and prove the limiting free energy for all non-critical temperature. We also
Some rigorous results on the Sherrington-Kirkpatrick spin glass model
• Physics
• 1987
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(ZN({βJ})) converges