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Transport measurements are carried out on dice Josephson-junction arrays withthe frustration index $f=1/3$ and 1/2 which possess, within the limit of the$XY$ model, an accidental degeneracy of the ground states as a consequence ofthe formation of zero-energy domain walls. The measurements demonstrate thatboth the systems undergo a phase transition to a superconducting vortex-orderedstate at considerably high temperatures. The experimental findings are inapparent contradiction with the theoretical expectation that frustrationeffects in the $f=1/3$ system are particularly strong enough to suppress avortex-ordering transition down to near zero temperature. The data for $f=1/2$are more consistent with theoretical evaluations. The agreement between theexperiments and the Monte Carlo simulations of a $XY$ model for $f=1/3$suggests that the order-from-disorder mechanism for the removal of anaccidental degeneracy may still be effective in the $f=1/3$ system. Thetransport data also reveal that the dice arrays with zero-energy domain wallsexperience a much slower critical relaxation than other frustrated arrays onlywith finite-energy walls.

Superconducting phase transitions in frustrated Josephson-junction arrays on a dice lattice