XY model with random p -fold anisotropy: Dynamics and statics near two dimensions

The phase structure and renormalization-group behavior of the XY model in a random p-fold anisotropy is studied via time-dependent Langevin formulation. The dynamics and statics are derived in two dimensions and extended to 2+ε dimensions. We find that a spin-glass-like phase at intermediate length scales becomes paramagnetic at large length scales as a result of the unbinding of vortices. In 2+ε dimensions a pure XY-type transition occurs for p²>8 into a low-temperature quasi-spin-glass phase with a finite susceptibility. A random-bond interaction is generated via renormalization.