Phase diagram of the spin-3/2 Blume-Capel model in three dimensions

We use a thermodynamically self-consistent theory to obtain the phase diagram of the ferromagnetic spin-3/2 Blume-Capel model on the simple cubic lattice. The theory is based on an Ornstein-Zernike approximation where the direct correlation function is truncated and the dependence upon the thermodynamic variables is determined by a set of two coupled partial differential equations. Within this framework, we localize the critical line in zero external field with high accuracy and in good agreement with previous Monte Carlo analysis. At low temperature, in contrast with Monte Carlo results, we find a first-order transition line ending at a critical end point whose coordinates are given by (k(B)T(c)/Jc=0.213+/-0.003,Delta(c)/Jc=0.491+/-0.001).