Based upon the spin wave theory, the spontaneous magnetization of small particle system at low temperatures is studied by means of solving the Heisenberg model directly. Investigations show that the spin waves are frozen out at ultra-low temperature, and the Bloch T3/2 law is no longer correct in any region of temperature. At the same time, the distribution of the probability for spins to be activated versus positions is obtained, which indicates that there exists no spin layers with obviously high probability to flip.