which is a rational approximant to $1-g$. Here, in the case of UFXY model, DT argues that the low temperature vortex configuration has lattice periodicity which is of order $q_{0}^{2}$, [*i.e.*]{}, much larger than $q_0$. On the other hand, in the case of LCG, GTG [@gtg] showed, via Monte Carlo (MC) simulations, that the low temperature charge configurations are characterized by arrangements of diagonal stripes that are either completely filled, completely empty, or partially filled with charges that are quite different from those vortex configurations in the corresponding UFXY model. However, GTG did not enumerate the exact patterns of low temperature charge configurations (such as spatial periodicity) for general cases of dense charge filling. In this work, we find that, for the values of $f$ between $1/3$ and $2/5$, there exist a simple regularity in the low temperature charge configuration which consists of periodic arrangements of combinations of two out of three types of striped charge patterns (see Section III).

For wide range of quenching temperatures above the first order transition $T_c$, the equilibrium relaxation continues to slow down with lowering temperature, and the form of the relxations are characterized by the stretched exponential with temperature-dependent exponents. Moreover, we observe 