Tricriticality and the Blume-Capel model: A Monte Carlo study within the microcanonical ensemble

The microcanonical partition function ${\Omega }_{\alpha ,N}\mathrm{}\left(E\right)\mathrm{}$ of a three-dimensional ferromagnetic simple cubic Blume-Capel model is calculated for several coupling ratios $\alpha$ close to and on the first-order side of the tricritical point. To this end a single Monte Carlo simulation of a suitably extended partition function for systems of $L\times L\times L$ spins with $L\in \{8,10,12,14,18\}$ was performed. A finite system analog of the latent heat is introduced in order to define a tricritical point in finite systems as well. An empirical scaling of its coordinates to the thermodynamic limit yields ${\alpha }^{\mathrm{}\left(t\right)\mathrm{}}=2.844\mathrm{}79\pm 0.00030$ for the tricritical coupling ratio, and $k_B{T}^{\mathrm{}\left(t\right)\mathrm{}}/J=1.4182\mathrm{}\pm 0.0055$ for the tricritical transition temperature. The results are compared with values obtained on fcc lattices.