Phase Diagram of the Antiferromagnetic Blume-Capel Model on Triangular Lattice

We perform Monte-Carlo simulations of the anti-ferromagnetic (AF) spin-1 Blume-Capel (BC) model and the AF Ising model on triangular lattice. We estimate the exact critical magnetic fields for both models at zero temperature using the Wang-Landau sampling method. We also show the phase diagrams and the critical lines for the models using the joint density functions. We find that the shapes of critical lines for the models are identical, but the phase transitions across the critical lines are different.