Heisenberg antiferromagnets on the Kagome lattices will be studied for quantum spins at large spin values and for classical spins at low temperature. Starting from the spin-wave approximation with anharmonic terms, effective Hamiltonians will be found expressing selection of (1) coplanar states, out of a continuum of degenerate classical ground states, and, (2) a particular ordered state, out of the discrete infinity of coplanar ground states. This ongoing work will be extended to study dilution disorder, spin tunneling, and (in the Kagome case) interlayer couplings. Certain discrete spin models in two dimensions can be mapped to solid-on-solid models in higher dimensions. Monte Carlo will be used to study the constrained Potts model, a new family of this type in higher dimension. The degree of order in the ground state of the spin one-half triangular antiferromagnet near the Ising limit will also be studied. %%% This theoretical research will focus on properties of frustrated antiferromagnets. The PI is a former Presidential Young Investigator. Frustrated antiferromagnets are of interest for a variety of reasons. The new high temperature superconductors are antiferromagnets in their normal state and this antiferromagnetism is thought to possibly play a role in producing their unique superconducting properties. The role played by the competition between disorder and magnetism in determining the properties of magnetic materials is a basic one which has eluded explanation. Finally, the statistical mechanics of novel lattice systems is also of basic interest.
