the other hand, it is easy to ensure stability of bcc(111) surface at zero coverage ( $\epsilon_{i} =0$) by choosing $\epsilon^{BB}_{3}<0$ and $\epsilon^{BB}_{4}<0$. Thus, there is general possibility to chose a set of interactions $\{\epsilon^{BB}_{3},  
 \epsilon^{BB}_{4}, \epsilon_{3},  \epsilon_{4}\}$ in such a way that at zero coverage the bcc(111) surface is stable whereas for coverage equal to one physical monolayer the bcc(211) surface become stable.

It is worth noting that surface energies per site $E_{hkl}$ are related to surface energies per surface atom $\sigma_{hkl}$(used in first principles calculation [@mad99b; @leung97]) in the following way $ \sigma_{111}= 3 E_{111}$, $ \sigma_{211}=2 
E_{211}$, $\sigma_{110}=E_{110}$, as the number of surface atoms is $N/3$, $N/2$, and $N$, respectively. Moreover, above stability conditions correspond to faceting conditions [@mad99b; @leung97] expressed in terms of scaled $\sigma_{hkl}$, e.g., the conditions $E_{211} \leq E_{111}$, $E_{211} \leq E_{110}$ are equivalent to $3\sigma_{211}/2\leq 
\sigma_{111}$, $3\sigma_{211}/2\leq 3\sigma_{110}$ for transformation $(111)\rightarrow \{112\}$.

Independence of stability condition on parameters $J_0$, $J_1$, and $K_1$ comes from assumptions on constant number of adsorbate atoms A and the restriction on column heights. Therefore we neglect these parameters in further analysis what corresponds to shifting of the surface energy by $-E_r$. Moreover, by choosing $J_2$ as the unit 