Two-dimensionalXYmodel with multiple symmetry-breaking fields

A generalization of the José, Kadanoff, Kirkpatrick, and Nelson (JKKN) model to multiple symmetry-breaking fields in the classical two-dimensional (2D) XY model is achieved by applying symmetry arguments to the renormalization-group equations. The generalized model is analyzed with the use of a renormalized spin-wave–vortex-gas technique, with finite-size effects included. Numerical examples of the generalized model are given for the case of a classical 2D XY model with a onefold symmetry-breaking field and a sixfold symmetry-breaking field. Applications of the generalized JKKN model are discussed in connection with the susceptibility measurements on ${\mathrm{CoCl}}_2$ intercalated graphite.