Spin and Chiral Orderings of the Antiferromagnetic XY Model on the Triangular Lattice and Their Critical Properties

We study the antiferromagnetic XY model on a triangular lattice by extensive Monte Carlo simulations, focusing on its ordering and critical properties. Our result clearly shows that two separate transitions occur at two distinct temperatures, the one at a higher temperature is associated with a Z₂-symmetry breaking driven by the chirality, and the one at a lower temperature is associated with the onset of the quasi-long-range order of the XY spin. We carefully examine the critical properties of each transition to find that the criticality of the chiral transition is consistent with the standard two-dimensional Ising universality class, whereas that of the spin transition might differ from the conventional Kosterlitz--Thouless (KT) one. The observed non-KT nature of the spin criticality is consistent with the most recent simulation result on the fully-frustrated XY model on a square lattice.