  Phase coherence and vortex order in the fully frustrated XY model on a
two-dimensional honeycomb lattice are studied by extensive Monte Carlo
simulations using the parallel tempering method and finite-size scaling. No
evidence is found for an equilibrium order-disorder or a spin/vortex-glass
transition, suggested in previous simulation works. Instead, the scaling
analysis of correlations of phase and vortex variables in the full equilibrated
system is consistent with a phase transition where the critical temperature
vanishes and the correlation lengths diverge as a power-law with decreasing
temperatures and corresponding critical exponents $\nu_{ph}$ and $\nu_{v}$.
This behavior and the near agreement of the critical exponents suggest a
zero-temperature transition scenario where phase and vortex variables remain
coupled on large length scales.
