Phase transition in the two-dimensional Coulomb gas, and the interfacial roughening transition

The behavior of the interface in the three-dimensional (3-D) Ising and related lattice systems is modeled using a 2-D array of columns of varying heights. We show that the "roughening" transition (the transition from a localized to a delocalized interface) is directly related to the metal-insulator transition in a 2-D Coulomb gas. Implications of this relationship are discussed.