The quantum J1−J2 Blume–Capel model

Abstract

In this study, it is investigated the effect of quantum fluctuations on the $J_1-J_2$ Blume–Capel model. The cluster mean field theory in the four site approximation is used to find the minimal (free) energy solutions. The ground state and finite temperature phase diagrams for the model with competitive ferromagnetic nearest neighbors ($J_1$) and antiferromagnetic next nearest neighbors interactions ($J_2$) are explored. It is found that the nature of phase transitions changes when quantum fluctuations and single-ion anisotropy parameter are varied. It is discussed the existence of tricritical points.