Crystal statistics with long-range forces: I. The equivalent neighbour model
Abstract
The aim of this series of papers is to help bridge the gap in our knowledge of the properties of the Ising and Heisenberg models between very short-range forces corresponding to nearest-neighbour interactions, and very long-range forces corresponding to the mean-field approximation. The present paper is concerned with the equivalent neighbour model in which the interactions between a spin and a certain finite number of its neighbours are equal, and the remaining interactions are all zero. Methods derived previously for obtaining series expansions at high temperatures are generalized to include second- and third-neighbour shells for standard two- and three-dimensional lattices. It is found that as the co-ordination number q increases the properties of the model approach an asymptotic value which depends on dimension, and on q in a given dimension, but not significantly on the type of lattice structure. An estimate is made of this asymptotic behaviour as a function of q.
- Publication:
-
Proceedings of the Physical Society
- Pub Date:
- December 1966
- DOI:
- 10.1088/0370-1328/89/4/311
- Bibcode:
- 1966PPS....89..859D