The phase transition in the antiferromagnetic stacked triangular lattices with classical XY spins interacting via antiferromagnetic nearest and next-nearest-neighbor bonds, $J_{1}$ and $J_{2}$, is studied by means of extensive histogram Monte Carlo simulations. When $J_{2}=0$, the transition is of second order with critical exponents slightly different from those given by other authors. It is shown that in a range of $J_{2}$, the transition is of first order. The general phase diagram in the $(J_{2}, T)$ space ($T$: temperature) is shown and discussed.[ pdf] [ postscript.gz]

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