ISING TRANSITION IN THE CLASSICAL ANNNXY MODEL

We investigate the XY model with ferromagnetic nearest and antiferroma gnetic next-to-nearest neighbours couplings (ANNNXY model). We formula te the study of both phases of the model in terms of different Coulomb gas models. The non-frustrated ferromagnetic phase is thus transforme d into a usual Coulomb gas with one species, whereas the frustrated ph ase is translated into a Coulomb gas with three species interacting wi th each other in an anisotropic lattice. We then generalize the Koster litz-Thouless renormalization group equations for both phases by treat ing the Ising and Kosterlitz-Thouless order parameters in an independe nt way. This enables us to discuss the nature of the transition (Ising and (or) Kosterlitz-Thouless) in the frustrated phase.