Phase transitions in classical two-dimensional lattice Coulomb gases

We carry out Monte Carlo simulations of the two-dimensional classical neutral Coulomb gas of integer charges on a square and a triangular lattice, and find rich phase diagrams as a function of temperature and chemical potential. At high densities, the ground state becomes a periodic charge lattice, and we find evidence suggesting that the melting transitions of these charge lattices are not always in the universality class expected from symmetry analysis. We compute the inverse dielectric constant ε^-1, which vanishes at the ``metal-insulator'' transition of the Coulomb gas. When the ground state is a charge vacuum, we find that ε^-1 is well described by the Kosterlitz-Thouless (KT) theory. When the ground state is a charge lattice, a larger than the KT universal jump in ε^-1(Tc) may be present. We also carry out simulations of the f=1/2 and 1/3 fractional Coulomb gas on a triangular lattice, and find similar results.