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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 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

Bibliographical note

Publisher Copyright:
© 2019 ALEA, Lat. Am. J. Probab. Math. Stat.

Keywords

Disorder chaos
Sherrington-Kirkpatrick model
Spin glass

Publisher link

10.30757/ALEA.V16-29

Find It

Find It at U of M Libraries

Cite this

@article{fd816bce8646484abf11bbca5c31a15c,

title = "Order of fluctuations of the free energy in the SK model at critical temperature",

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).",

keywords = "Disorder chaos, Sherrington-Kirkpatrick model, Spin glass",

author = "Chen, {Wei Kuo} and Lam, {Wai Kit}",

note = "Publisher Copyright: {\textcopyright} 2019 ALEA, Lat. Am. J. Probab. Math. Stat.",

year = "2019",

doi = "10.30757/ALEA.V16-29",

language = "English (US)",

volume = "16",

pages = "809--816",

journal = "Alea",

issn = "1980-0436",

publisher = "Instituto Nacional de Matematica Pura e Aplicada",

number = "1",

}

TY - JOUR

T1 - Order of fluctuations of the free energy in the SK model at critical temperature

AU - Chen, Wei Kuo

AU - Lam, Wai Kit

PY - 2019

Y1 - 2019

N2 - 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).

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

UR - http://www.scopus.com/inward/record.url?scp=85069988019&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069988019&partnerID=8YFLogxK

U2 - 10.30757/ALEA.V16-29

DO - 10.30757/ALEA.V16-29

M3 - Article

AN - SCOPUS:85069988019

SN - 1980-0436

VL - 16

SP - 809

EP - 816

JO - Alea

JF - Alea

IS - 1

ER -

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

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this