A Monte Carlo study of the Ising model with uniaxial anisotropy

Monte Carlo simulations are used to study the cubic Ising model with uniaxial anisotropy. The coexistence curve of the model is first determined as a function of the coupling anisotropy parameter. Except for large anisotropy, the coexistence curve scales to a single parameter identifiable as the mean coupling environment. Accurate measurements of the critical temperature as a function of anisotropy agree well with previous renormalisation group work. A study is then made of the shapes and size distribution of stable phase droplets in the metastable state well below the critical point. An analysis of the droplet moments of inertia shows that they flatten as the anisotropy is increased. It is found that the size distribution of the deformed droplets can be described by classical nucleation theory, provided the droplet surface tension is reinterpreted as a surface averaged quantity.