Dynamics of the generalized Glauber-Ising chain in a magnetic field |
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Authors: | A Baumgärtner K Binder |
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Institution: | (1) Theoretische Physik, Universität, Saarbrücken, West Germany |
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Abstract: | A one-dimensional kinetic Ising model with nearest neighbor interactionJ and magnetic fieldH 0 is treated in both linear and nonlinear response, using the most general single spin-flip transition probabilities that depend on nearest neighbor states only. The dynamics is reformulated in terms of kinetic equations for the concentration nl
+(t) @#@ nl(t) of clusters containingl up- or down-] spins, which is exact in the homogeneous case. The initial relaxation time * of the magnetization is obtained rigorously for arbitraryJ, H, and temperatureT. The relaxation function is found by numerical integration forJ/T < 2. It is shown that coagulation of minus-clusters becomes negligible for bothJ/T andH/T large, and the resulting set of equations is solved exactly in terms of an eigenvalue problem. A perturbation theory is developed to take into account the neglected coagulation terms. The relaxation function is found to be non-Lorentzian in general, in contrast to the Glauber results atH = 0, which are recovered as a special case. In addition, nonlinear and linear relaxation functions differ forH 0. Consequences for the application to biopolymers are briefly mentioned.Supported in part by the Deutsche Forschungsgemeinschaft (SFB 130). |
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Keywords: | Ising model master equation clusters nonlinear response relaxation functions biopolymers |
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