Some rigorous results on the Sherrington-Kirkpatrick spin glass model

M. Aizenman; J. L. Lebowitz; D. Ruelle

doi:10.1007/BF01217677

Some rigorous results on the Sherrington-Kirkpatrick spin glass model

M. Aizenman, J. L. Lebowitz, D. Ruelle

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165 Scopus citations

Abstract

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})) converges in distribution, as N → ∞, to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.

Original language	English (US)
Pages (from-to)	3-20
Number of pages	18
Journal	Communications In Mathematical Physics
Volume	112
Issue number	1
DOIs	https://doi.org/10.1007/BF01217677
State	Published - Mar 1987
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01217677

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title = "Some rigorous results on the Sherrington-Kirkpatrick spin glass model",

abstract = "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 in distribution, as N → ∞, to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.",

author = "M. Aizenman and Lebowitz, {J. L.} and D. Ruelle",

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AU - Ruelle, D.

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N2 - 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 in distribution, as N → ∞, to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.

AB - 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 in distribution, as N → ∞, to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.

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Some rigorous results on the Sherrington-Kirkpatrick spin glass model

Abstract

All Science Journal Classification (ASJC) codes

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