Monte Carlo study of the fcc Blume-Capel model

We have used a Monte Carlo method to study the face-centered-cubic (fcc) Blume-Capel model: $\mathcal{H}=-J\Sigma {\mathrm{}\left(\mathrm{ij}\right)\mathrm{}}^{}{S}_{\mathrm{iz}}{S}_{\mathrm{jz}}+\Delta \Sigma i^{}{S}_{\mathrm{iz}}^2+H\Sigma i^{}{S}_{\mathrm{iz}}$, where $S=1\mathrm{}$ and the sum ($\mathrm{ij}$) is over the $q=12\mathrm{}$ nearest neighbors. We have traced out the $\Delta -T$ phase boundary and have found a tricritical point at $\frac{k{T}_t}{\mathrm{qJ}}=0.256\mathrm{}\pm 0.004$. The tricritical behavior is consistent with the classical behavior of the Riedel-Wegner Gaussian fixed point. We have also traced out the tricritical "wings" in $\Delta -T-H$ space and have found their critical behavior to be consistent with three-dimensional Ising exponents.