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

The microcanonical partition function Omega(alpha,N)(E) 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 LxLxL spins with L is an element of {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((t))=2.84479+/-0.00030 for the tricritical coupling ratio, and k(B)T((t))/J=1.4182+/-0.0055 for the tricritical transition temperature. The results are compared with values obtained on fee lattices.