Effective field renormalization group approach to classical antiferromagnets on d-dimensional corner-sharing hyper-tetrahedral lattices

Abstract

A real-space renormalization group method for classical interacting spins on a d-dimensional lattice of corner-sharing hyper-tetrahedra is presented. These include the classical Heisenberg model on the kagome and pyrochlore lattices as particular cases. The partition function of clusters of different sizes and the corresponding order parameters are calculated to leading order in the symmetry breaking fields created by the spins outside the cluster and the corresponding scaling relations and critical behavior of these lattices are analyzed. To illustrate the simplicity of the method, a reduced subset of the possible ordered states of these lattices for the isotropic nearest-neighbour interaction problem is studied in detail. It is found that the method correctly predicts the absence of the ordered state on the antiferromagnetic sector of the model no matter the dimensionality of the lattice or the number of spin components. Possible ways to consider more complex ordered states and higher-order effects —such as order by disorder— in the present framework are also discussed.