  There is empirical evidence that the two-point correlation function of the
galaxy distribution follows, for small scales, reasonably well a power-law
expression $\xi(r)\propto r^{-\gamma}$ with $\gamma$ between 1.5 and 1.9.
Nevertheless, most of the point field models suggested in the literature do not
have this property.
  This paper presents a new class of models, which is produced by modifying
point fields commonly used in cosmology to mimic the galaxy distribution, but
where $\gamma=2$ is too large. The points are independently and randomly
shifted, leading to the desired reduction of the value of $\gamma$.
