We investigate the ground state of the irrationally frustrated Josephson junction array with controlling anisotropy parameter lambda that is the ratio of the longitudinal Josephson coupling to the transverse one. We find that the ground state has one dimensional periodicity whose reciprocal lattice vector depends on lambda and is incommensurate with the substrate lattice. Approaching the isotropic point, lambda=1 the so called hull function of the ground state exhibits analyticity breaking similar to the Aubry transition in the Frenkel-Kontorova model. We find a scaling law for the harmonic spectrum of the hull functions, which suggests the existence of a characteristic length scale diverging at the isotropic point. This critical behavior is directly connected to the jamming transition previously observed in the current-voltage characteristics by a numerical simulation. On top of the ground state there is a gapless, continuous band of metastable states, which exhibit the same critical behavior as the ground state.
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