Polymers in media with long-range-correlated quenched disorder

We study the scaling properties of self-avoiding walks (SAWs) on a d-dimensional disordered lattice with quenched defects obeying a power law correlation similar to r(-a) for large distances r. Such type of disorder is known to be relevant for magnetic phase transitions. We apply the field-theoretical renormalization group approach and perform calculations in a double expansion in epsilon = 4 - d, delta = 4 - a. The asymptotic behaviour of SAWs on a lattice with long-range-correlated disorder is found to be governed by a new exponent v(long) = 1/2 + delta /8 (epsilon /2 < <delta> < <epsilon>). This is to be compared with the first order result for SAWS on a "pure" lattice: v(pure) = 1/2 + epsilon /16, (epsilon > 0). (C) 2001 Elsevier Science B.V. All rights reserved.