Node-avoiding Lévy flight: A numerical test of the epsilon expansion.
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We study an extension of L\'evy flight to include self-repulsion in the path of the walk. We call the extension node-avoiding L\'evy flight and we show its equivalence to the $n\ensuremath{\rightarrow}0$ limit of a statistical mechanical model for a magnetic system with long-range interactions between the spins. By use of this equivalence we are able to make a detailed comparison between the results of the $\ensuremath{\epsilon}$ expansion for the magnetic model, a Monte Carlo simulation of the L\'evy flight model, and the results of a Flory-type argument. This is the first comparison of the $\ensuremath{\epsilon}$ expansion for $\ensuremath{\epsilon}\ensuremath{\ll}1$ with a numerical simulation for any model. Some speculations are made on applications of the model of node-avoiding L\'evy flight.