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We present Monte Carlo simulation results on the equilibrium relaxationdynamics in the two dimensional lattice Coulomb gas, where finite fraction $f$of the lattice sites are occupied by positive charges. In the case of highorder 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 systemexhibits, for wide range of temperatures above the first-order transition, aglassy behavior resembling the primary relaxation of supercooled liquids.Single particle diffusion and structural relaxation show that there exists abreakdown of proportionality between the time scale of diffusion and that ofstructural relaxation analogous to the violation of the Stokes-Einsteinrelation in supercooled liquids. Suitably defined dynamic cooperativity iscalculated to exhibit the characteristic nature of dynamic heterogeneitypresent in the system.Comment: 12 pages, 20 figure

Structural relaxation, self-diffusion, and kinetic heterogeneity in the two-dimensional lattice Coulomb gas