Analytical approximations for the hierarchically constrained kinetic Ising chain |
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Authors: | S. Eisinger J. Jäckle |
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Affiliation: | (1) National College of Safety Engineering, Haugesund, Norway;(2) Fakultät für Physik, Universität Konstanz, Konstanz, Germany |
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Abstract: | ![]() The hierarchically constrained kinetic Ising model in one dimension is reviewed, and the results of several analytical approaches to the model are presented. Two standard approximation schemes, an effective-medium approximation and a mode-coupling approximation, are shown to fail. A new class of approximations, termed cluster approximations, is better suited for the model. It yields good results for the spin autocorrelation function, and also elucidates important general properties of the model—its connection with defect-diffusion models and the asymptotic long-time behavior of the autocorrelation function. |
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Keywords: | Ising models kinetic constraint effective-medium approximation mode-coupling approximation cluster approximation long-time behavior |
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