  Phase coherence and vortex order in a Josephson-junction array at irrational
frustration are studied by extensive Monte Carlo simulations using the parallel
tempering method. A scaling analysis of the correlation length of phase
variables in the full equilibrated system shows that the critical temperature
vanishes with a power-law divergent correlation length and critical exponent
$\nu_{ph}$, in agreement with recent results from resistivity scaling analysis.
A similar scaling analysis for vortex variables reveals a different critical
exponent $\nu_{v}$, suggesting that there are two distinct correlation lengths
associated with a decoupled zero-temperature phase transition.
