Xy and Xy-ising Models

We consider the 2D J 1 −J 2 classical XY model on a square lattice. In the frustrated phase corresponding to J 2 > J 1 /2, an Ising order parameter emerges by an " order due to disorder " effect. This leads to a discrete symmetry plus the O(2) global one. We formulate the problem in a Coulomb gas language and show by a renormalization group analysis that only two phases are still possible: a locked phase at low temperature and a disordered one at high temperature. The transition is characterized by the loss of Ising and XY order at the same point. This analysis suggests that the 2D J 1 − J 2 XY model is in the same universality class than XY-Ising models.