By considering a magnetic system of an ensemble of nanometer clusters without any exteal magnetic field, the Monte Carlo simulation of the Heisenberg model is used to investigate the transition from a superparamagnetism to a ferromagnetic single-domain state, which is caused by the growth of the clusters. We studied the variation of the dynamic growth exponent P and the transition critical size of the cluster Nc against the reduced temperature t and the uniaxial anisotropy constant A. We found that the growth exponent maximized at a certain temperature,other than being taken as a universal constant as some researchers suggested previously.