On growth walks with self-avoiding constraints

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Abstract
The authors study a general class of growth walks in two dimensions with a self-avoiding constraint, which can be considered as 'dressed' self-avoiding walks. A walker travels on a square lattice and chooses at each step one of the three forward directions with probability p1, p2 and p3 if the directions are allowed. The self-avoiding constraint is obtained by 'dressing' the walk with 'black' and 'white' particles after each step such that the walk generates the external perimeter of arbitrary clusters consisting of black or white particles. They discuss the critical values of p1, p2 and p3 which allow for infinite walks and study the end-to-end distance r(t) and the corresponding distribution function N(r, t). Furthermore, they introduce a bias field in growth process and discuss how the time evolution of the walk is modified by the bias.