Coupled-cluster approximation for spin lattices: Application to solidHe3

We have extended the coupled-cluster approximation to the spin-lattice problem. The efficiency of this method is demonstrated on simple antiferromagnetic Heisenberg models in one and two dimensions. We then apply it to the problem of the ground state of the spins of solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the presence of multiple spin exchanges. The first-order transition field between the two ordered phases is calculated, using the exchange parameters determined from first principles. Its variations as a function of the molar volume are predicted.