Self-attracting walk with nu <1/2

A model of a self-attracting walk is proposed. Mean square displacement of a particle xi grows with time t as a power law xi 2 approximately t 2 nu with the exponent nu <1/2. It is shown that nu =1/(2D-D b ) where D is the fractal dimension of the cluster consisting of the visited 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 obtained by computer simulation.