The Dependence Structure of Hamiltonians of the SK-Model

Zhaoxu Wang; Xijuan NIu

doi:10.20944/preprints202402.1058.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 19 February 2024 / Approved: 19 February 2024 / Online: 20 February 2024 (06:10:20 CET)

The SK model proposed by Sherrington and Kirkpatrick is an important mean field model for spin glasses. The dependence structure of Hamiltonians of the SK model is considered in this paper. We have investigated the covariance matrix of Hamiltonians of the SK model, and establish a relationship between the rank of the corresponding covariance matrix and the dimension of the space spanned by the Hamiltonians. Finally, we also give an upper bound for the rank of the covariance matrix, which might be the best.

SK model; Hamiltonians; rank; covariance matrix

Computer Science and Mathematics, Probability and Statistics

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The Dependence Structure of Hamiltonians of the SK-Model

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