Abstract: Using the renormalization-group transformation method together with the cumulative expansion technique, the phase transition and critical properties of the S⁴ model on a type of hierarchical lattice were studied, and its fixed points and critical exponents were obtained. The results show that there exists a Wilson-Fisher fixed point besides the Gaussian fixed point, compared with those of the S⁴ model on the special diamond-type of hierarchical lattices, the critical points and critical exponents have changed. It has been found that both of them belong to different university classes.

Key words: hierarchical lattice, S⁴ model, renormalization-group, critical properties