First-order interface localization-delocalization transition in thin Ising films using Wang-Landau sampling.

Using extensive Monte Carlo simulations, we study the interface localization-delocalization transition of a thin Ising film with antisymmetric competing walls for a set of parameters where the transition is strongly first order. This is achieved by estimating the density of states (DOS) of the model by means of Wang-Landau sampling (WLS) in the space of energy, using both single-spin-flip as well as N-fold way updates. From the DOS we calculate canonical averages related to the configurational energy, like the internal energy and the specific heat, as well as the free energy and the entropy. By sampling micro-canonical averages during simulations we also compute thermodynamic quantities related to magnetization like the reduced fourth-order cumulant of the order parameter. We estimate the triple temperatures of infinitely large systems for three different film thicknesses via finite size scaling of the positions of the maxima of the specific heat, the minima of the cumulant, and the equal weight criterion for the energy probability distribution. The wetting temperature of the semi-infinite system is computed with help of the Young equation. In the limit of large film thicknesses the triple temperatures are seen to converge toward the wetting temperature of the corresponding semi-infinite Ising model in accordance with standard capillary wave theory. We discuss the slowing down of WLS in energy space as observed for the larger film thicknesses and lateral linear dimensions. In the case of WLS in the space of total magnetization we find evidence that the slowing down is reduced and can be attributed to persisting free energy barriers due to shape transitions.