Phase and vortex correlations in Josephson-junction arrays at irrational frustration

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.