Magnetic correlations on fractals |
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Authors: | Amnon Aharony Yuval Gefen Yacov Kantor |
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Institution: | (1) Department of Physics and Astronomy, Tel Aviv University, 69978 Tel Aviv, Israel;(2) Institute of Theoretical Physics, University of California, 93106 Santa Barbara, California;(3) Exxon Corporate Research Laboratories, Route 22E, 08801 Annandale, New Jersey |
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Abstract: | The critical behavior of magnetic spin models on various fractal structures is reviewed, with emphasis on branching and nonbranching Koch curves and Sierpiriski gaskets and carpets. The spin correlation function is shown to have unusual exponential decays, e.g., of the form exp-(r/gx)
x
], and to crossover to other forms at larger distancesr. The various fractals are related to existing models for the backbone of the infinite incipient cluster at the percolation threshold, and conclusions are drawn regarding the behavior of spin correlations on these models. |
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Keywords: | Spin models percolation fractals renormalization group magnetic correlations |
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