Universality of node-avoiding and path-avoiding Levy flights

Abstract

The real space renormalisation group theory is applied to the self-avoiding Levy flight problem with Levy exponent mu on a two-dimensional square lattice. A finite-lattice renormalisation transformation is used to derive the critical behaviour exhibited by two classes of self-avoiding Levy processes: the node-avoiding Levy flight (NALF); the path-avoiding Levy flight (PALF). It is found that the NALF and the PALF belong to the same universality class.