Multiple-spin-exchange calculation of theT=0properties of solidHe3

The multiple-exchange Hamiltonian used to describe spin-spin interactions in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is developed in terms of Pauli spin operators for an arbitrary number of particles in the exchange cycle. The T=0 mean-field properties of the ‘‘up-up-down-down’’ ($U_2$ $D_2$) and canted normal antiferromagnetic magnetic phases are then calculated including two-, three-, four-, five-, and six-particle exchange processes. These properties agree well with experimentally determined melting-curve values when evaluated using the exchange frequencies calculated by Ceperley and Jacucci.