Employing the Monte Carlo simulation technique, we have investigated several phase transitions exhibited by a coupled XY model in two dimensions. The model is based on the Hamiltonian proposed by Bruinsma and Aeppli [Phys. Rev. Lett. 48, 1625 (1982)]. The simulation results demonstrate the existence of a new type of phase transition in which two different orderings are simultaneously established through a continuous transition. The unique nature of this phase transition provides a plausible explanation for our recent high-resolution heat-capacity data near the smectic-A-hexatic-B transition of two-layer free-standing films.
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