Monte Carlo study of the fcc Blume-Capel model

Abstract

We have used a Monte Carlo method to study the face-centered-cubic (fcc) Blume-Capel model: $\mathcal{H}=\ensuremath{-}J\ensuremath{\Sigma}{(\mathrm{ij})}^{}{S}_{\mathrm{iz}}{S}_{\mathrm{jz}}+\ensuremath{\Delta}\ensuremath{\Sigma}{i}^{}{S}_{\mathrm{iz}}^{2}+H\ensuremath{\Sigma}{i}^{}{S}_{\mathrm{iz}}$, where $S=1$ and the sum ($\mathrm{ij}$) is over the $q=12$ nearest neighbors. We have traced out the $\ensuremath{\Delta}\ensuremath{-}T$ phase boundary and have found a tricritical point at $\frac{k{T}_{t}}{\mathrm{qJ}}=0.256\ifmmode\pm\else\textpm\fi{}0.004$. 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 $\ensuremath{\Delta}\ensuremath{-}T\ensuremath{-}H$ space and have found their critical behavior to be consistent with three-dimensional Ising exponents.