Effect of long cyclic exchanges on the magnetic properties of bcc 3He

Using path-integral Monte Carlo calculations, we have calculated ring exchange frequencies in the bcc phase of solid He-3 for densities from melting to the highest stable density. We evaluate 42 different exchange frequencies from two atoms up to eight atoms and find their Gruneisen exponents. Using a fit to these frequencies, we calculate the contribution to the Curie-Weiss temperature, Theta(CW), and upper critical magnetic field, B-c2, for even longer exchanges using a lattice Monte Carlo procedure. We find that contributions from seven-and eight-particle exchanges make a significant contribution to Theta(CW) and B-c2 at melting density. Comparison with experimental data is given.