Vortex state of a 2D Josephson junction array at irrational frustration

IV characteristics of a 2D Josephson junction array are studied experimentally at frustrations f=0.382, as an approximation of the irrational filling f=(3-√5)/2, and its nearby rationals 3/8, 8/21, and 2/5, with a focus on the irrational frustration. For all four frustrations, the IV characteristics exhibit a scaling behavior, indicating a finite-temperature continuous superconducting transition. Scaling analyses show that the critical behaviors for f=0.382 are similar to those of f=3/8, 8/21, and 2/5. The finite transition temperature and the similarity in critical behaviors suggest that the vortex state at the irrational frustration is not a vortex glass but possibly an ordered phase with a configuration which can be viewed as an interpolation between the states for f=3/8 and 2/5