Exchange frequencies in the 2D Wigner crystal

Using path integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2D Wigner crystal as a functi on of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarka bly, the exchange Hamiltonian closely resembles the measured exchanges in 2 D He-3. Using the resulting multispin exchange model we find the spin Hamil tonian for r(s) less than or equal to 175 +/- 10 is a frustrated antiferrom agnetic; its likely ground state is a spin liquid. For lower density the gr ound state will be ferromagnetic.