We see that non-exponentiality increases as the temperature decreases. These results clearly indicate that the equilibrium relaxation in the 2D LCG above $T_c$ closely resembles the primary relaxation of typical fragile liquids.

One of the main characteristic features of the single particle dynamics is described by the mean square displacement $\langle (\Delta \vec r)^2 \rangle$, which is defined as

$$\langle (\Delta \vec r)^2 \rangle = \langle \sum_{j=1}^{N_Q}
 (\vec{r}_j(t)-\vec{r}_j(0))^2 \rangle / N_Q,$$

where $\vec{r}_j(t)$ is the position vector of the $j$-th charge at time $t$ and $N_Q$ the total number of charges. Figure 5 shows $ \langle (\Delta \vec r)^2 \rangle $ for various temperatures. It exhibits an early time subdiffusive regime and crosses over into late time diffusive regime. Early time subdiffusive behavior is thought to be coming from local frustrated motions of charges before reaching an average displacement of unit lattice spacing. To test the proportionality of the two time scales, the structural relaxation time scale $\tau$ and the diffusion time scale $D^{-1}$, we plot the temperature dependence of the product $4 D\tau$ in Fig. 6. Here, we clearly see that the breakdown of the proportionality between the two time scales is observed for wide range of temperatures below 