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Journal of Physics C Solid State Physics

Average metastable states and internal fields in Ising spin glasses

Muhammad H. Ahmed

Published Dec 20, 1982• 0 citations
Publisher

Abstract

The Thouless, Anderson and Palmer equations of Ising spin glasses of the Sherrington and Kirkpatrick model have been solved numerically for a finite system size. The distribution of internal magnetic fields, average of logarithm of metastable states and logarithm of average metastable states have been evaluated down to energy ranges where correlation between metastable states develops.

DOI
10.1088/0022-3719/15/35/004

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The Thouless, Anderson and Palmer equations of Ising spin glasses of the Sherrington and Kirkpatrick model have been solved numerically for a finite system size. The distribution of internal magnetic fields, average of logarithm of metastable states and logarithm of average metastable states have been evaluated down to energy ranges where correlation between metastable states develops.
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These notes give an introduction to the physics of the infinite range version of the Edwards--Anderson model, the so-called Sherrington--Kirkpatrick model. In a first part, I motivate and introduce the Edwards--Anderson and Sherrington--Kirkpatrick models. In the second part, I explain the analytical solution of the Sherrington--Kirkpatrick model, following Giorgio Parisi. I next give the physical interpretation of this solution. This is a vast subject, and I concentrate on the major points and give references for more details. The third part presents the simulation approach and compare its results to theoretical expectations: thermodynamics, finite size scaling, determination of the critical temperature using "parameters" like the "Binder parameter", and fluctuations. The last part gives a summary of our current understanding of finite size effects for the free energy and internal energy of the Sherrington--Kirkpatrick model
Abstract. Numerical results for the local field distributions of a family of Ising spinglass models are presented. In particular, the Edwards-Anderson model in dimensions two, three, and four is considered, as well as spin glasses with long-range powerlaw-modulated interactions that interpolate between a nearest-neighbour Edwards-Anderson system in one dimension and the infinite-range Sherrington-Kirkpatrick model. Remarkably, the local field distributions only depend weakly on the range of the interactions and the dimensionality, and show strong similarities except for near zero local field. PACS numbers: 75.50.Lk, 75.40.Mg, 05.50.+qLocal field distributions in spin glasses 2 1.
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