The two- and three-dimensional spin-3/2 random Blume–Capel model by the position space renormalization group

We use the Migdal–Kadanoff renormalization group technique to study the spin-3/2 Blume–Capel model under a random crystal field, in the two- and three-dimensional cases. Studying the fixed points and the phase diagrams established, we find interesting results allowing us to understand the critical behavior of the system. In the two-dimensional case, the randomness, even in small amounts, removes completely the first order transition between the two ferromagnetic phases present, replacing it by a smooth continuation. Only the second order phase transitions occur. In the three-dimensional case, the first order phase transition disappears only at a certain threshold of randomness. Below this threshold, we observe the presence of an end-point where finishes the first order transition line inside the ferromagnetic phases. This end-point reaches T=0K at a critical value of probability, beyond which only the second order transitions occur.