Abstract
A recently proposed model for self-attracting walks is studied using exact enumeration techniques. The probability of a step is proportional to exp(-nu), where n=1 for sites already visited by the walker and n=0 for the others, with u<0. Series for the mean-square displacement (RN2) approximately N2 nu and the mean number of visited sites (SN) approximately Ns of N-step walks are calculated in one to four dimensions. In all dimensions anomalous diffusion is observed, and exponents nu and s vary continuously with the strength parameter u: The results are compared with simulations and with previous results for static and dynamic models of generalized random walks in one dimension. The behaviour in two and three dimensions may describe anomalous diffusion in real systems.
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