not attempt a detaled analysis (including a finite size scaling) of the histogram, we think that this estimate value of the transition temperature should not be considered too seriously for its precision.

We find empirically that there exist a simple regularity in the low temperature charge configuration in LCG (Fig. 3). For the case of values of $f$ in the range $1/3 \leq f \leq 2/5$, it is found that the low temperature configuration becomes quasi-one-dimensional with periodic striped patterns. In the cases of $f=1/3$ and $f=2/5$ the ground state configurations are identical to the low temperature vortex configurations in the UFXY model. However, for values of $f$ in between $1/3$ and $2/5$, the low temperature patterns are found to be, unlike the case of corresponding UFXY model, consisting of periodic arrangements of combinations of two out of three types of striped charge patterns as follows.

First component pattern (type I pattern) is a sequence of three diagonals which are [*empty, filled*]{}, and [*empty*]{} respectively (that may be denoted by [**(010)**]{} in our notation where [**1**]{} refers to a filled diagonal and [**0**]{} refers to an empty diagonal). In other words, it is a pattern with single isolated diagonal filled 