Frustrated magnets: A Monte Carlo study of stiffness, vorticity and topological excitations

The role of topological excitations in frustrated Heisenberg antiferromagnets between two and three spatial dimensions is studied as well as the controversial issue of the order of the phase transition of Heisenberg and XY frustrated antiferromagnets in 3d. The antiferromagnetic Heisenberg model on a stacked triangular geometry with a finite number of layers is studied using Monte Carlo methods. The symmetry of the ordered phase of this model admits the existence of the same type of topological defect as in the superfluid B phase of He3. A phase transition which is purely topological in nature occurs at finite temperature for all film thicknesses. The results indicate that topological excitations are important for a complete understanding of the critical properties of the model between two and three dimensions. The rigidity properties of the stacked triangular Heisenberg antiferromagnet are studied in 3d using both a heat bath and a broad histogram Monte Carlo method. The results are consistent with a continuous transition and a direct estimate of the correlation length critical exponent nu from the spin stiffness yields the value nu = 0.59 in agreement with a newly proposed 'chiral' universality class. A generalized model for the XY antiferromagnet is introduced and studied in 3 d using heat bath Monte Carlo methods. The model can be continuously tuned from a region of first order transitions to the usual XY model without changing its symmetry properties. The results unambiguously show that the phase transition in XY frustrated antiferromagnets in 3d is weakly first order. Further work is needed in 3 d to clarify the order of the transition in the Heisenberg case and the role played by topological excitations.