Monte Carlo study of the two-dimensional vector Blume-Capel model

The Blume-Capel model (BCM) generalizes the Ising model to allow for the presence of vacancy sites, and was used as an early description of the effect of a He-3 admixture on the He-4 superfluid transition, especially tricritical behavior. The vector counterpart of the BCM improves upon the original by utilizing spins with a continuous symmetry, the correct universality class for superfluidity. This paper presents a Monte Carlo calculation of the full phase diagram of the two-dimensional vector BCM. A tricritical point is shown to separate a first-order phase transition line at low temperature from a Kosterlitz-Thouless boundary at higher temperature and the location of the tricritical point is determined.