Analog of surface preroughening in a two-dimensional lattice Coulomb gas

Elaborating on previous theoretical treatments of the roughening transition, we provide the exact mapping of a surface model which undergoes both roughening and preroughening onto a mixture of unit and double charges living on the square lattice. Depending on the model parameters, the preroughening transition of the surface can be either continuous or discontinuous. Using the surface temperature as a control parameter, the dual Coulomb gas accordingly undergoes two consecutive phase transitions through equilibrium phases whose dielectric behavior is analysed in terms of Monte Carlo simulation and exact finite-size calculations. Right at the preroughening point of the surface model, the charged mixture behaves like an electric insulator (provided preroughening is second-order), while showing metallic behavior below and above that temperature, at least up to the roughening temperature where the conventional metal-insulator transition occurs.