T=0 {#s2_stab}
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First, we will check the stability of ideal surfaces (111), (211), and (110) covered with 3, 2, 1 geometric monolayers of A, similarly as it was performed in first principles calculations [@leung97]. This allows us to estimate values of model parameters for reconstruction, from (111) surface to $\{112\}$ or to $\{011\}$ faceted surface, under assumption that edge energies are neglected.

Using the Hamiltonian Eq. (\[hsos\]) we get the following expressions for surface energy per site for ideal face of orientation $(hkl)$

$ \displaystyle E_{111}= E_{r} + 7 J_2$,

$ \displaystyle E_{110}= E_{111}+ 2 J_2 + 2 K_2$,

$ \displaystyle E_{211}= E_{111}+  K_2$,

where

$ \displaystyle E_{r}= J_0 + K_1 + 2 J_1$.

Thus, the stability conditions are:

$K_2 \geq 0$, $ J_2 +K_2 \geq 0 \;\;$ for (111) surface,

$ J_2 +K_2 \leq 0$, $ 2 J_2 +K_2 \leq 0\;\;$ for (110) surface,

$K_2 \leq 0$, $ 2 J_2 +K_2 \geq 0\;\;$ for (211) surface.

It easy to see that transformation from (111) surface to {211} facets will be possible for negative values of $K_2$ and appropriate positive $J_2$. To satisfy these conditions, the range of interactions $\epsilon^{\alpha \beta}_{i}$ should be not smaller than $r_4=a \sqrt{11}/2$. On 