Abstract: The growth probabilities {P_α,i} and configuration weights C_α (for 2×2 cell and 3×3 cell) are obtained by using the renormalization-group method. The "partition function" Z(q,L), "Free energy" F(q,L),"energy" E(q,L),"specific heat" c(q,L) and hierarchical dimensions D_q are calculated. The evidence has been found for suggesting the existence of phase transition in the multifractal spectrum of the SPA model and position of critical point q_c=0. In the words, the distribution of growth probability has no multifractal features.

Key words: fractal, renormalization-group, phase transition