Low-Temperature Behavior of a Pure Dipole-Dipole System

Abstract

The Van Vleck moment expansion is applied to a pure dipole system. On the basis of the long-range nature of the forces, sequences of diagrams are selected that give the dominant contributions in the lattice sums. A selection of diagrams contributing to the entropy and susceptibility is displayed. There are three different summations to be performed for each type of diagram: the trace over the spin variables, the lattice summation, and the summation over the Cartesian coordinates. The second was performed on a computer, and the last is obtained by means of the Kramers-Wannier diagonalization. In order, to obtain the contributions of diagrams of higher order, a Fourier transform is employed. The calculations are performed for cerous magnesium nitrate using a $g$ factor that is zero along the $c$ axis. The results are compared with experiments. The susceptibility $\chi$ was calculated for a uniform and for a nonuniform field, and it is suggested that the critical temperature is determined by the infinity of $\chi \mathrm{}\left(q\right)\mathrm{}$ for $q\ne 0$, rather than by that of $\chi \mathrm{}\left(0\right)\mathrm{}$.