Phase boundaries of a spin-3/2 Blume–Emery–Griffiths model on a honeycomb lattice

• We study the spin-3/2 Blume–Emery–Griffiths model on a honeycomb lattice.
• We employ Monte Carlo simulations to determine phase diagrams.
• Finite-size scaling is used to identify transition order and universality class.
• We find second-order transitions with weakly- or nonuniversal behavior.
• Multiple phase boundary steps observed by effective-field theory are not confirmed.

The spin-3/2 Blume–Emery–Griffiths model on a honeycomb lattice is studied by Monte Carlo simulations with the goal to determine phase diagrams for a range of the model parameters and to investigate the nature of the phase transitions between the respective phases. For positive values of the biquadratic to bilinear interaction ratio α, we find two ferromagnetically ordered phases, F1 and F2, with the sublattice magnetizations (1/2,1/2)(1/2,1/2) and (3/2,3/2)(3/2,3/2), respectively, and our results confirm the discontinuous character of the order-disorder critical line as a function of the single-ion anisotropy strength, predicted by the effective-field theory (EFT). For negative values of α  , there is another ferrimagnetic phase of the type (1/2,3/2)(1/2,3/2), located between F1 and F2. However, the step-like variation of the order-disorder critical frontier obtained from EFT for large negative α   is not reproduced and thus deemed artifact of the EFT approximation. Finite-size scaling analysis performed at various points between the respective identified phases gave the ratio of critical exponents γ/νγ/ν consistent with the 2D Ising universality class, except in the vicinity of the boundary intersection, where the results deviated from the standard values beyond the measurement errors.