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Path Integral Monte Carlo is used to calculate exchange frequencies as electrons undergo ring exchanges in a "clean" 2d Wigner crystal as a function of density. Agreement with WKB calculations is found at very low density, but the results show an enhanced increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d 3  He . Using the resulting multi-spin exchange model we find the spin Hamiltonian for r s  ≥ 175 ± 10 is a frustrated antiferromagnetic, with a spin liquid ground state. For lower density the ground state will be ferromagnetic. Some effects of a magnetic field are presented.

EXCHANGE FREQUENCIES IN THE 2D WIGNER CRYSTAL