  A simple solid-on-solid model of adsorbate-induced faceting is studied by
using a modified Wang-Landau method. The phase diagram for this system is
constructed by computing the density of states in a special two-dimensional
energy space. A finite--size scaling analysis of transition temperature and
specific heat shows that faceting transition is the first order phase
transition. Logarithmic dependence of the mean-square width of the surface on
system size indicates that surface is rough above the transition temperature.
