Critical behavior of the one-dimensional S=1 XY model with single-ion anisotropy

We study the quantum critical behavior of the one-dimensional, S=1 XY model in the presence of a single-ion anisotropy. Using a path-integral approach, we obtain, at T=0 and for a positive anisotropy constant, a classical free-energy functional that allows discussion of the critical properties. The rescaling of frequencies is governed by the critical exponent z=1. Renormalization-group arguments reveal that at criticality the system belongs to the same universality class as the isotropic 2-d XY model. © 1984 The American Physical Society.