Structural Relaxation, Self Diffusion and Kinetic Heterogeneity in the Two Dimensional Lattice Coulomb Gas

We present Monte Carlo simulation results on the equilibrium relaxation dynamics in the two dimensional lattice Coulomb gas, where finite fraction $f$ of the lattice sites are occupied by positive charges. In the case of high order rational values of $f$ close to the irrational number $1-g$ ($g\equiv(\sqrt{5} -1)/2$ is the golden mean), we find that the system exhibits, for wide range of temperatures above the first-order transition, a glassy behavior resembling the primary relaxation of supercooled liquids. Single particle diffusion and structural relaxation show that there exists a breakdown of proportionality between the time scale of diffusion and that of structural relaxation analogous to the violation of the Stokes-Einstein relation in supercooled liquids. Suitably defined dynamic cooperativity is calculated to exhibit the characteristic nature of dynamic heterogeneity present in the system.