SELF-ATTRACTING WALK WITH V-LESS-THAN-1 2

A model of a self-attracting walk is proposed. Mean square displacemen t of a particle xi grows with time t as a power law xi2 approximately t2nu With the exponent nu < 1/2. It is shown that nu = 1/(2D - D(b)) w here D is the fractal dimension of the cluster consisting of the visit ed sites and D(b) is the fractal dimension of its boundary. A compact cluster with fractal boundaries was obtained by a computer simulation for d = 2. The derived value of nu is in a good agreement with that ob tained by computer simulation.