Topological defects in the fully frustrated XY model and in³He-A films

The ground states of both the fully frustrated XY model in two dimensions and 3 He-A films have Z 2 *U(1) symmetries. Both line defects (domain walls) and point defects (vortices) can disrupt ordering in these systems at finite temperatures. The presence of line defects induces a breakdown on vortex charge quantisation in both of these systems. In the fully frustrated XY model on a square lattice, integral quantisation of charge is replaced by quarter-integral quantisation; in 3 He-A, quantisation of charge is completely destroyed. It follows that in both of these systems phase ordering cannot coexist with Z 2 disorder. The fully frustrated XY model is relevant to Josephson junction arrays in a transverse magnetic field, at a value of the field where half of a magnetic flux quantum threads each cell of the array.