Abstract
Abstract We study the scaling properties of self-avoiding walks (SAWs) on a d -dimensional disordered lattice with quenched defects obeying a power law correlation ∼ 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 e = 4 − d , δ = 4 − a . The asymptotic behaviour of SAWs on a lattice with long-range-correlated disorder is found to be governed by a new exponent ν long = 1/2 + δ/8, (e/2 pure = 1/2 + e/16, (e > 0).
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