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We study the antiferromagnetic {\it XY} model on a triangular lattice byextensive Monte Carlo simulations, focusing on its ordering and criticalproperties. Our result clearly shows that two separate transitions occur at twodistinct temperatures, the one at a higher temperature is associated with a$Z_2$-symmetry breaking driven by the chirality, and the one at a lowertemperature is associated with the onset of the quasi-long-range order of the{\it XY} spin. We carefully examine the critical properties of each transitionto find that the criticality of the chiral transition is consistent with thestandard two-dimensional Ising universality class, whereas that of the spintransition might differ from the conventional Kosterlitz-Thouless (KT) one. Theobserved non-KT nature of the spin criticality is consistent with the mostrecent simulation result on the fully-frustrated {\it XY} model on a squarelattice.

Spin and chiral orderings of the antiferromagnetic XY model on the triangular lattice and their critical properties