Vortices and strings: Phase transition in anisotropic planar-rotor systems

We have investigated the phase transition of a two-dimensional system described by the Hamiltonian H = -J summation/sub NN/ cos(theta/sub i/-theta/sub j/)-K summationNN cos(theta/sub i/+theta/sub j/+phi/sub ij/), for J,K>0 and 0< or =K/J< or =1, and where NN denotes nearest neighbors, which has both Ising-like domain-wall (string) and XY-like vortex excitations. Migdal-Kadanoff and Monte Carlo renormalization-group studies indicate that there is only one transition which is Ising-like. The roles of string and vortex excitations in the phase transition are discussed by an energy-entropy argument and are found to be consistent with Monte Carlo quench results