Low-Temperature Behavior of a Pure Dipole-Dipole System
- 1 May 1970
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 1 (9) , 3786-3800
- https://doi.org/10.1103/physrevb.1.3786
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 factor that is zero along the axis. The results are compared with experiments. The susceptibility was calculated for a uniform and for a nonuniform field, and it is suggested that the critical temperature is determined by the infinity of for , rather than by that of .
Keywords
This publication has 20 references indexed in Scilit:
- On the specific heat of paramagnetic salts at very low temperaturesPhysica, 1969
- Magnetic Interactions between Rare-Earth Ions in Insulators. II. Electron-Paramagnetic-Resonance Measurements of Pair and - Interaction Constants in EuPhysical Review B, 1969
- Thermal and magnetic properties of cerium magnesium nitrate below 1KPhysica, 1969
- Magnetic Interactions between Rare-Earth Ions in Insulators. I. Accurate Electron-Paramagnetic-Resonance Determination of Pair-Interaction Constants in LaPhysical Review B, 1968
- THE LOW-TEMPERATURE ORDERED STATE OF CERIUM MAGNESIUM NITRATE AND ITS INFLUENCE ON NUCLEAR ORIENTATIONCanadian Journal of Physics, 1964
- Spin WavesReviews of Modern Physics, 1958
- The Effect of Interactions in a Paramagnetic on the Entropy and SusceptibilityProceedings of the Physical Society. Section A, 1953
- High Temperature Susceptibility of Permanent Dipole LatticesThe Journal of Chemical Physics, 1953
- Dipoles on a Lattice : the Spherical ModelThe Journal of Chemical Physics, 1952
- Theory of Dipole Interaction in CrystalsPhysical Review B, 1946