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Self-Attracting Walk on Lattices

Jae Woo Lee
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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^{2ν}$ 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 $ν=k=1/2$. However, in two and three dimension, we observed a non-universal behaviour, i.e., the exponent $ν$ varies continuously with the strength of the attracting interaction.

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Jae Woo Lee. 1997-08-07. Self-Attracting Walk on Lattices. https://doi.org/10.1088/0305-4470%2F31%2F16%2F018

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