As the value of $f$ continuously increases within the two regimes (in the above), the system in the low temperature stable configuration simply adjusts itself by accomodating the extra charges into the partially filled diagonal channels and thereby changing the charge filling within the channels. The dividing value of $f=f_c \simeq 0.381$ between the two regimes appears to correspond to the value $8/21$ in which case the partially filled diagonals have filling density exactly equal to $2/3$. Our simulations show that the filling density $2/3$ inside the partially filled diagonal plays as a stability limit for the channel structures. Beyond this limit, electrostatic instability probably begins to set in, and rearrangement of the whole charge configuration occurs in order to form a new stable ordered patterns. As was also argued by GTG, in general, at much lower temperature $T_p$ (below $T_c$) the charges within the partially filled channels are expected to exhibit ordering, which would depend sensitively on rationality of the exact filling ratio of charges inside the partially filled diagonals.

An important aspect of our simulations is that one has to choose the lattice size appropriately in order to match the periodicity of the true low temperature configuration in 