REAL-SPACE RENORMALIZATION FOR HEISENBERG MODELS ON 2-DIMENSIONAL LATTICES

Real-space renormalization methods which simply shift and rescale the interaction parameters in the nearest-neighbor Heisenberg model are investigated for two-dimensional lattices of equivalent sites. Results are presented for the hexagonal, square-planar, triangular, and Kagome lattices via three different renormalization techniques. The first, which has been studied for some time, uses perturbation theory to evaluate the renormalized interactions. The second uses the variational method to improve on the perturbative results. The third method is based on a cluster expansion and is found to give much improved agreement with numerical results form Monte Carlo calculations, but it does not provide a variational bound to the exact solution. The dependence of all three methods on the size and shape of the renormalized block of sites is also investigated.