  We study a lattice model of a magnetic polymer where the XY spin variables
are located on a self-avoiding walk (SAW) on a regular lattice in two and three
dimensions. We consider the regime where both spins and conformations are
dynamic, thus the XY model is defined on a dynamic lattice and conformations
generate an annealed disorder. Using Monte Carlo simulations, we characterize
the globule-coil and ferromagnetic phase transitions, and pay special attention
to the vicinity of the theta-point. Our numerical results suggest that the
transitions are continuous in two dimensions and first-order in three
dimensions, which is similar to related models with Ising spins.
