in LEED experiment in Pd/Mo(111) system. However, it was suggested that coexistence is due to the inhomogeneity of the surface.

![ Plot of column height along the y direction for the surface: (a) below the phase transition, T=1.17, (b) above the phase transition, T=1.50, (c) ideal bc(111) - initial configuration. []{data-label="figure5"}](fig5){width="6cm"}

One of quantities measured in MC simulation is the square mean width of the surface, $${\delta h}^2 = 
  \left<   
    \frac{1}{N}    
      \sum\limits_{j} 
         {           
             \left( h_j  - \left<{h}\right>\right)^2                                                       
         }  
    \right>.$$ Behaviour of the $\delta h^2$ during warming up and cooling down processes allows us to study dependence of mean vertical sizes of pyramids on temperature. In Fig. \[figure6\] we present results of simulation for 3 different annealing times $\tau= 
2\times 10^3,\;2\times 10^4,\;3\times 10^5$. In all cases the hysteresis loop is present near the phase transition and for shorter time a larger hysteresis is observed. It is easy to explain because it is more probable to overcome the free energy barrier in longer time. In the warming up process the size of pyramids does not depends on the annealing time $\tau$ up to $T\approx 0.5$. When temperature approaches $T\approx 1$ then a rapid growth is observed and for longer annealing time $\tau$ 