Phase transitions of some fully frustrated models

Fully frustrated antiferromagnets with triangular plaquettes are investigated. For the two-dimensional triangular lattice, the Ising antiferromagnet is in the class of the XY model with transition temperature T=0. For d>or=3 the authors investigate the face-centred cubic lattice. For even d there is a proper phase transition with long-range order. For odd d the fluctuation spectrum has a reduced dimensionality (d-1). This is reflected in an infinite ground state degeneracy and a reduced dimensionality of the ground state order (d-n). For d=3 a phase transition occurs for the Ising model but not for n>or=3. The relationship of the fully frustrated phase to the disordered spin glass is also discussed. It is suggested that the two phases might be distinct near d=6 but coalesce at some lower dimensionality.