Migdal–Kadanoff solution of the mixed spin-1 and spin-3/2 Blume–Capel model with different single-ion anisotropies

•One type of phase diagrams where coexist first and second order transitions.•Two types of phase diagrams presenting only the second order transitions.•A tricritical line finishing by two end-points.•Absence of a dimensional crossover.

Using the real space renormalization group theory, we investigate the alternated mixed Blume–Capel model with spins S=1S=1 and S=3/2S=3/2, on the hyper cubic lattice. First, the ground state phase diagram of the system at zero temperature is obtained on the single-ion anisotropies plane showing the same topology obtained early by other approximations.According to the different values of the single-ion anisotropies, three types of phase diagrams are obtained, with first and second order transitions; tricritical points are highlighted. Also, we note the absence of dimensional crossover between d=2d=2 and d=3d=3.