  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 He.
Using the resulting multi-spin exchange model we find the spin Hamiltonian for
r_s \leq 175 \pm 10 is a frustrated antiferromagnetic; its likely ground state
is a spin liquid. For lower density the ground state will be ferromagnetic.
