system [@szuk02]. The phase transition between the disordered phase and one of ordered is of first order as surface energy, the square mean width of the surface $\delta 
h^2$, and the structure factor (see Sec. \[s5\]) change discontinuously at the transition point.

![ Phase diagram: T versus K. []{data-label="figure7"}](fig7){width="7cm"}

The transition temperature between F{211} and disordered phase is bounded from above by maximum $T_c=1.20$ at $K=-1.50$. If we chose this point to estimate model parameters for Pd/Mo(111) with $T_c=850$ K we get $J_2=0.06$ eV, and $K_2=-0.09$ eV. On the other hand the transition temperature from F{110} to the disordered phases is increasing function of $|K|$ and it might reach large value. The present model does not include the desorption, thus we can expect that transition temperature might be above the desorption temperature in some systems especially where the faceted F{110} phase occurs. In such cases the phase transition to the disordered faceted phase could not be observed but rather deconstruction induced by desorption would be expected.

There is difficult to study phase transition between ordered phases using MC simulation because for $K\approx -2$ we observed coexistence of two types of facets $\{011\}$ and $\{112\}$. The mixed phase does not contain 