  Transport measurements are carried out on dice Josephson-junction arrays with
the 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 of
the formation of zero-energy domain walls. The measurements demonstrate that
both the systems undergo a phase transition to a superconducting vortex-ordered
state at considerably high temperatures. The experimental findings are in
apparent contradiction with the theoretical expectation that frustration
effects in the $f=1/3$ system are particularly strong enough to suppress a
vortex-ordering transition down to near zero temperature. The data for $f=1/2$
are more consistent with theoretical evaluations. The agreement between the
experiments and the Monte Carlo simulations of a $XY$ model for $f=1/3$
suggests that the order-from-disorder mechanism for the removal of an
accidental degeneracy may still be effective in the $f=1/3$ system. The
transport data also reveal that the dice arrays with zero-energy domain walls
experience a much slower critical relaxation than other frustrated arrays only
with finite-energy walls.
