Phase transitions in the two-dimensional classical lattice Coulomb gas of half-integer charges

We carry out Monte Carlo simulations of the two-dimensional (2D) classical lattice Coulomb gas of half-integer charges on a square lattice, which is believed to be in the same universality class as the fully frustrated 2D XY model, and find evidence for two transitions. At the lower temperature, we find a Kosterlitz-Thouless-type transition with a larger than universal jump in the dielectric constant ${\mathrm{\epsilon }}^{\mathrm{-}1}$. At the higher temperature, we find a second-order charge lattice melting transition with a scaling behavior different from the pure Ising transition, in contrast to expectations from the symmetry analysis.