Phase transitions in Heisenberg antiferromagnets on triangular and layered-triangular lattices (invited)

Recent results on phase transitions of classical Heisenberg antiferromagnets on the (d=2)-dimensional triangular and the (d=3)-dimensional layered-triangular lattices are summarized. In the ground states, the spins are ordered into a ‘‘120° structure’’ in which the frustration is partially resolved by mutual spin canting. A symmetry argument shows that the order-parameter space associated with the ground state has a quite different topology from those of corresponding nonfrustrated systems being isomorphic to the three-dimensional rotational group SO(3) or the projective space P3. Homotopy analysis establishes that the system sustains a topologically stable vortex characterized by a two-valued topological quantum number: a Z2 vortex. A Monte Carlo study of the d=2 model suggests the occurrence of a novel type of topological phase transition driven by the dissociation of the Z2 vortices. For the corresponding d=3 model Monte Carlo indicates the occurrence of a single continuous transition; by use of finite-size scaling theory, the exponents are estimated to be α≂0.4, β≂0.25, γ≂1.1, and ν≂0.53. These values differ considerably from those for the standard nonfrustrated systems, strongly suggesting a phase transition belonging to a new universality class. Corresponding renormalization-group ε expansions have been carried out to O(ε2). In leading orders a frustration-dominated fixed point exists only for n-component spins with n>3 but for finite ε the corresponding fixed point might continue down to n=3 and ε=1. Several other systems exhibiting an SO(3)-like symmetry, including the superfluid A phase of helium 3 and certain helical or canted magnets, should belong to the same universality class. Possible consequences for experiments are discussed.