The Peierls inequality combined with a classical Monte Carlo evaluation of the free energy has been applied as a variational technique to the magnetic spin Hamiltonian of 3He. We find unexpectedly good agreement with the experimental phase diagram and other measured quantities.
We have applied a new approximation to the problem of 3He magnetism and found very good agreement with experiment.
Since Hetherington and Willard 1 following an early idea by Thouless 2 suggested that large ring exchange terms may play an important role in the magnetic properties of solid 3He at the miUiKelvin temperature range almost two decades ago, much progress has been made in this field both experimentally and theoretically. It is now believed that nuclear magnetic ordering in this system can be described with a multiple-spin-exchange Hamiltonian 3'4 by considering a few exchange processes. Recently using path-integral Monte Carlo technique Ceperley and Jacucci s were able to determine the exchange coefficients (for up to six spins) from first principles. Their calculated values confirmed that the most important types of exchange were indeed those considered previously (2, 3, and 4 spins). 3"6 However they found the six-spin exchanges were not negligible. Within mean field approximation, Godfrin and Osheroff 7 used Ceperley and Jacucci's coefficients to calculate magnetic properties at zero temperature. Although most three-dimensional localized magnetic systems, even if spin half, show fairly small quantum effects that are well accounted for by spin wave theory, there is abundant evidence that the quantum effects in the effective multiple-spin-exchange Hamiltonian of solid ~He are large.S-1ยฐ From the theoretical point of view, it is quite challenging to treat such a highly quantum spin system. Recently Roger and Hetherington 11 extended the coupled-cluster approximation (CCA) of this 303 0022-2291/92/0300-0303506.50/0 ~i~ 1992 Plenum Publishing Corporation