We investigate phase transitions of the XY model on a two-layer triang
ular lattice when interactions are competing, by using Monte Carlo sim
ulations. For the system with a ferromagnetic interaction on one of tw
o layers and an antiferromagnetic interaction on the other layer, we f
ind two different types of critical phenomena with two phase-transitio
n temperatures; (1) each of phase transitions due to chirality and (2)
the Kosterlitz-Thouless-type phase transition and a chirality transit
ion. We clarify the nature of these phase transitions by using finite-
size scaling analyses. (C) 1998 Elsevier Science B.V. All rights reser
ved.