Critical properties of directed self-avoiding walks

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Abstract
The generating functions and mean displacements of various two-dimensional directed self-avoiding walk models are calculated exactly by a simple transfer-matrix approach. Asymptotically, the authors find (R/sub //N/) approximately RN2)1/2 approximately N, and (Rperpendicular to N2)1 approximately N1/2, where N is the number of steps in the walk, and // and perpendicular to refer to projections of the displacement parallel and perpendicular to the preferred axis of the walk respectively. Some general properties of directed self-avoiding walks for arbitrary dimensions are discussed as well.