The Alexander-orbach Conjecture Holds in High Dimensions
نویسندگان
چکیده
We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior have been established, namely when the dimension d is large enough or when d > 6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension ds = 4 3 , that is, pt(x, x) = t . This establishes a conjecture of Alexander and Orbach [4]. En route we calculate the one-arm exponent with respect to the intrinsic distance.
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تاریخ انتشار 2009