as well as, zones with chessboard-like pattern [@goles]. The full patterns will be characterized by the global magnetization : $$\begin{aligned}
M(t)= M[\left\{x^t\right\}]  =  \sum_{k}  x^{t}_k ,
\label{magnetization}\end{aligned}$$ Naturally, the function $M$ is restricted to the interval $-N\leq M\leq N$, and the available values of $M$ are ranged in uniform steps of $\Delta M =2$.

A detailed characterization of the evolution, as well as, of the fluctuations of the magnetization has been treated in detail in Ref. [@goles]. Briefly, after a transient the average magnetization depends mainly on the initial energy. If the energy is low, one sees that the average magnetization evolves slowly in time to an “equilibrium” state with an almost constant value plus weak fluctuations. For larger energies, the fluctuations enter to play an important role. One may observe that the system is in an almost stable state, but then suddenly jumps into a metastable state with zero average magnetization, and then jumps into an opposite magnetization state [@goles].

The plot of the temporal average of the global magnetization versus the energy is done in Fig. \[MvsE\]. One sees that the magnetization spontaneously increases below a critical energy per site around $E_c/N = - 1.4$, close to the 