Self-Attracting Walk on Lattices

Abstract

We have studied a model of self-attracting walk proposed by Sapozhnikov using Monte Carlo method. The mean square displacement $<R^2(t)>\sim t^{2\nu }$ and the mean number of visited sites $<S(t)>\sim t^k$ are calculated for one-, two- and three-dimensional lattice. In one dimension, the walk shows diffusive behaviour with $\nu =k=1/2$. However, in two and three dimension, we observed a non-universal behaviour, i.e., the exponent $\nu$ varies continuously with the strength of the attracting interaction.

6 pages, latex, 6 postscript figures, Submitted J.Phys.A

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