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 .