On the magnetically dilute Heisenberg and Ising ferromagnetics
- 1 January 1961
- journal article
- research article
- Published by Taylor & Francis in Molecular Physics
- Vol. 4 (1) , 1-15
- https://doi.org/10.1080/00268976100100011
Abstract
The lowering of the Curie temperature of a ferromagnetic substance by random dilution with non-magnetic elements is studied on the basis of Heisenberg and Ising models having nearest-neighbour interactions between magnetic elements only. It is proved that the limiting concentration, p c, of magnetic elements, below which there is no Curie temperature, is the same for all such models, whether Heisenberg or Ising and regardless of the spin value concerned: it depends only on the lattice structure. Numerical estimates of p c are given for various lattices. Successive approximations are developed to the full Curie temperature curve, and it is found that whereas for the Ising model T c(p) approximates to pT c(1) near p=1, T c(p)<pT c(1) for the Heisenberg model.Keywords
This publication has 8 references indexed in Scilit:
- Statistical Mechanical Theory of a Random Ferromagnetic SystemPhysical Review B, 1959
- Remarks on magnetically dilute systemsJournal of Physics and Chemistry of Solids, 1959
- Cluster Sums and Related Coefficients of the Ising ModelProgress of Theoretical Physics, 1958
- Susceptibility and Curie Point of Magnetically Dilute CrystalsThe Journal of Chemical Physics, 1957
- On the susceptibility of a ferromagnetic above the Curie pointProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1957
- On the High-Temperature Susceptibility for the Heisenberg Model of a FerromagnetProceedings of the Physical Society. Section A, 1955
- Statistics of the Three-Dimensional Ferromagnet (III)Journal of the Physics Society Japan, 1951
- On the exchange interaction in magnetic crystalsPhysica, 1937