Renormalisation theory of the self-avoiding Levy flight

Abstract

The self-avoiding Levy flight (SALF) in d dimensions with Levy exponent mu is formulated as a geometrical equilibrium statistical mechanical problem. A direct renormalisation theory, based on modern field theoretic techniques, is used to derive the critical exponents and the end-to-end distance probability function through first order in epsilon =2 mu -d. The non-perturbative structure of the probability function is characterised by a universal scaling function. The SALF represents a simple many-body system that can assume a continuum of values of epsilon near zero.