Random symmetry-breaking fields and theXYmodel

The two-dimensional classical XY model in a random p-fold symmetry-breaking field is studied using the replica method. For p>2√2 an XY like phase exists at intermediate values of temperature and weak field. For p≤4 we are able to describe the transition into the low-temperature glassy continuation of the paramagnetic phase, while for $p>4$ the results suggest the transition may be first order, driven by the unbinding of vortices. Several new fixed points and lines are found in the replicated Kosterlitz-Thouless-type recursion relations corresponding to these various transitions. The method we use considers n coupled XY models from which we construct a Coulomb gas with n(n-1)2 types of (n-1)-dimensional vector charges.