The unbinding of kink pairs on domain walls in the fully frustrated $\mathrm{XY}$ model (on square or triangular lattices) is shown to induce the vanishing of phase coupling across the walls. This forces the phase transition, associated with unbinding of vortex pairs, to take place at a lower temperature than the other phase transition, associated with proliferation of the Ising-type domain walls. The results are applicable for a description of superconducting junction arrays and wire networks in a perpendicular magnetic field, as well as of planar antiferromagnets with a triangular lattice.

• Received 1 June 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.167007