Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
