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: $H={-}J{Σ}{(ij)}^{}{S}iz{S}jz+{Δ}{Σ}{i}^{}{S}iz²+H{Σ}{i}^{}{S}iz$, where $S=1$ and the sum ($ij$) is over the $q=12$ nearest neighbors. We have traced out the ${Δ}{-}T$ phase boundary and have found a tricritical point at ${k{T}ₜ}{qJ}=0.256±{}0.004$. 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 ${Δ}{-}T{-}H$ space and have found their critical behavior to be consistent with three-dimensional Ising exponents.