Abstract. A self-avoiding walk on a lattice may be characterised by the 'excluded volume ratio' V=closest approach of two centres/stop length. Walks to other than nearest-neighbour sites on a simple cubic lattice have high coordination numbers and low values of the excluded volume ratio. Some general results are presented for a class of these walks. Exact enumerations and Monte Carlo simulations have been made of the total number C_N and the mean square length (R_N²) for two examples of this class. These measurements are used to test the 'universality hypothesis' which contends that C_N approximately N^1/6 mu ^N and (R_N²) approximately N^6/5 as N to infinity , irrespective of the value of V. The data are in reasonable agreement with these statements, and the universality hypothesis is found to provide a good basis for the description of a self-avoiding walk.

Print publication: Issue 5 (1 May 1980)