slightly increases, there are more points where the faceted and disordered phases coexist but it seems that sizes of pyramids do not depend on the temperature increment.

We observe that the growth of the facets on warming base on formation of a larger pyramid from several smaller pyramids. Probability of such rebuilding of the surface is very small at low temperature. This is reflected in the acceptance ratio $f$, a fraction of accepted configurations in the Markov chain, which is very low at low temperatures, $f \approx 0.002$ below $T=0.3$ and $f=0.01$ at $T=0.7$. On the other hand, the acceptance ratio is of the same order for $T=1.0$, $f=0.1$, and close to the phase transition, $f=0.2$, but we observe difference in facets sizes at these temperatures. Looking at snapshots of the surface after annealing at temperature up to $T\approx 1.1$ on warming, we found that pyramids have nearly ideal shapes (see for example Fig. \[figure3\]). We think that all above observation can be explained in the following way. The system is passing through metastable states - local minima of the free energy - as temperature is increased. There are barriers between local minima hence the growth of facets depends on 