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 function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2D (3)He. Using the resulting multispin exchange model we find the spin Hamiltonian for r(s) < or = 175 +/- 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.