the thermodynamic limit. If, otherwise, one chooses a lattice size that is incommensurate with the periodicity (of striped patterns), then one ends up with defective charge configurations with patches of local ground state configurations. We think that this is probably why GTG got two different equilibrium configurations when two different lattice sizes $L=26$ and $L=52$ are used for $f=5/13$ since these $L$’s turn out to be incommensurate with the true periodicity $l_p =12$.

When the screening length $\lambda$ is finite, then we find the low temperature configuration becomes different from the case of no screening ($\lambda \rightarrow \infty$) in such a way that the partially filled diagonals gets rarer. The influence of the screening effect on the statics and the relaxation dynamics needs further study.

Equilibrium relaxation dynamics
-------------------------------

We now discuss the equilibrium relaxation dynamics of the model above first order transition. In order to probe the structural relaxation of charges, we measured the on-site charge autocorrelation functions,

$$C(t)=\langle \sum_{i=1}^{N} Q_i(0)Q_i(t) \rangle / N,$$

where the bracket $< \cdots >$ represents an average over different random initial configurations.

Shown in Fig. 4a is the on-site charge autocorrelation function $C(t)$ for temperatures from $T=0.1$ down to $T=0.033$. From this figure, 