RENORMALIZATION OF RANDOM-WALKS WITH MEMORY

The renormalisation of field-theoretic models of the 'true' self-avoiding random walk is analysed. For short-range interactions, the field theory is shown to be renormalisable only in a special case, which corresponds to the problem of a random walk in a random environment, and non-renormalisable otherwise. The long-range version of the field theory is shown to be renormalisable in a larger region of the parameter space. In the case which corresponds to the original long-range 'true' self-avoiding random walk, the renormalisation group analysis is carried out to two-loop order. Anomalous dimensions of various composite operators are calculated and the crossover between scaling regimes described by short-range and long-range models is discussed.