Order of fluctuations of the free energy in the SK model at critical temperature

Wei Kuo Chen; Wai Kit Lam

doi:10.30757/ALEA.V16-29

Order of fluctuations of the free energy in the SK model at critical temperature

Wei Kuo Chen, Wai Kit Lam

Mathematics

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3 Scopus citations

Abstract

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 at the critical temperature the variance of the free energy is of O((logN)²): In addition, we show that if one approaches the critical temperature from the low temperature regime at the rate O(N^-α) for some α > 0; then the variance is of O((logN)² + N^1-α).

Original language	English (US)
Pages (from-to)	809-816
Number of pages	8
Journal	Alea
Volume	16
Issue number	1
DOIs	https://doi.org/10.30757/ALEA.V16-29
State	Published - 2019

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© 2019 ALEA, Lat. Am. J. Probab. Math. Stat.

Keywords

Disorder chaos
Sherrington-Kirkpatrick model
Spin glass

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abstract = "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 at the critical temperature the variance of the free energy is of O((logN)2): In addition, we show that if one approaches the critical temperature from the low temperature regime at the rate O(N-α) for some α > 0; then the variance is of O((logN)2 + N1-α).",

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AU - Lam, Wai Kit

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AB - 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 at the critical temperature the variance of the free energy is of O((logN)2): In addition, we show that if one approaches the critical temperature from the low temperature regime at the rate O(N-α) for some α > 0; then the variance is of O((logN)2 + N1-α).

KW - Disorder chaos

KW - Sherrington-Kirkpatrick model

KW - Spin glass

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Order of fluctuations of the free energy in the SK model at critical temperature

Abstract

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Keywords

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