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

The microcanonical partition function Ω_α,N(E) of a three-dimensional ferromagnetic simple cubic Blume-Capel model is calculated for several coupling ratios α 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×L×L spins with L∈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 α⁽ᵗ⁾=2.84479±0.00030 for the tricritical coupling ratio, and kBT⁽ᵗ⁾/J=1.4182±0.0055 for the tricritical transition temperature. The results are compared with values obtained on fcc lattices.