The 2D J₁ - J₂ XY and XY-Ising models

Laboratoire de Physique Théorique et Hautes Energies Universités Pierre et Marie Curie Paris VI et Denis Diderot Paris VII, 2 pl. Jussieu, 75251 Paris Cedex 05, France

Received: 30 January 1997
Accepted: 5 June 1997

Abstract

We consider the classical XY model on a square lattice. In the frustrated phase corresponding to , 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  XY model is in the same universality class as XY-Ising models.