XY model on a self-avoiding walk.

We study a lattice model of a magnetic polymer where the XY spin variables are located on a self-avoiding walk 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 are similar to related models with Ising spins.