$f$.

Simulation Results and Discussions
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First order transition and low temperature configuration
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We first discuss the equilibrium phase transition and charge configuration of the system. As was first shown by GTG, we also find that there exist a first order transition in LCG with $f$ near $1-g$. Figure 1 shows temporal snapshots of charge configurations evolving from disordered state into ordered configuration after being quenched to a temperature $T=0.026$. First order nature of the phase transition can easily be confirmed by enumerating the histogram of energies $P(E)$ near the transition temperature [@sw]. $P(E)$ is obtained by counting the occurrences of energies for each of the equally spaced energy bins while performing the equilibrium Monte Carlo simulations (via simple Metropolis algorithm). For a system with first order transition, the energy histogram $P(E)$ becomes bimodal near the transition temperature corresponding to a mixture of ordered state (with lower energy) and a disordered state (with higher energy). The transition temperature $T_c$ can be determined by locating the temperature where the subareas under the two peaks are equal. Figure 2 shows two histograms near the transition temperature, where we could estimate the transition temperature approximately as $T_c \simeq 0.0316$. Since we did 