Self-avoiding Lévy walk: A model for very stiff polymers

We propose a non-Markovian extension of the Lévy walk model of Shlesinger and Klafter [Phys. Rev. Lett. 54, 2551 (1985)], termed self-avoiding Lévy walk, to study a polymer configuration having a broad persistance length distribution. We use the Flory-type argument in a manner analogous to the self-avoiding walk and the self-avoiding Lévy flight schemes to include the excluded-volume effect and find that the Flory exponent ${\nu }_{\mathit{F}}$ varies continuously from the flexible limit [${\nu }_{\mathit{F}}$=3/(d+2)] to the stiff limit (${\nu }_{\mathit{F}}$=1), when the spatial dimension d and the Lévy index μ are varied. We also discuss the fractal dimensions and the morphology of Lévy walks in comparison with the Lévy flights.