Dynamics of Ising spin glasses far below the lower critical dimension: The one-dimensional case and small clusters |
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Authors: | J. D. Reger K. Binder |
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Affiliation: | (1) Institut für Festkörperforschung der Kernforschungsanlage Jülich, Postfach 1913, D-5170 Jülich 1, Federal Republic of Germany;(2) Present address: Institut für Physik, Johannes-Gutenberg-Universität Mainz, Postfach 3980, D-6500 Mainz, Federal Republic of Germany;(3) Institut für Festkörperforschung der Kernforschungsanlage Jülich, Federal Republic of Germany |
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Abstract: | The Glauber model is studied for symmetric distributions (±J and gaussian) of the nearest-neighbour interactionJ, including a magnetic field. For small clusters of spins (closed rings ofN bonds, withN7) the complex magnetic susceptibility () and the time-dependent remanent magnetizationm(t) are found exactly for given bond configurations {Jij} by diagonalization of the Liouville operator; apart from the ±J model, the average over {Jij} must be done numerically by simple random sampling Monte Carlo. Nevertheless our accuracy is much better than corresponding dynamic Monte Carlo simulations, even if one considers the extrapolation toN.We analyze the results along the lines of corresponding experimental work, studying the frequency-dependence of the peak in (), theT lnt-scaling ofm(t) at low temperaturesT, and the decomposition of () into a spectrum of relaxation times. Many results are strikingly similar to experimental data for systems such as the Holmium-Borate spinglass or the superparamagnet Eu0.05Sr0.95S, for instance. Frequency-dependent critical fieldsHc() in theH-T plane are also identified but do not have the familiar Almeida-Thouless shape, however.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday |
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