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.
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机译：我们通过广泛的蒙特卡洛模拟研究三角网格上的反铁磁{\ it XY}模型，重点是其有序性和临界性质。我们的结果清楚地表明，在两个不同的温度下发生两个单独的跃迁，一个较高的温度与由手性驱动的$ Z_2 $-对称断裂有关，而一个较低的温度与准长的发生有关{\ it XY}旋转的-range顺序。我们仔细检查了每个过渡的临界性质，发现手性过渡的临界性与标准的二维Ising通用性类别一致，而自旋转变的临界性可能与传统的Kosterlitz-Thouless（KT）有所不同。所观察到的自旋临界的非KT性质与在全晶格上完全受挫的{\ it XY}模型上的最新仿真结果一致。
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