Abstract
The exact solution of the three-dimensional Ising model of a ferromagnetic presents difficulties of a very fundamental nature. It therefore seems that the most reliable information on the behaviour of the model is provided by exact series expansions of the partition function at low and high temperatures. However, the usual low -temperature expansion fails to converge in the neighbourhood of the critical point. By rearranging the terms of the series on the basis of physical considerations, it is possible to obtain a systematic set of successive approximations, each approximation taking exact account of clusters of a given size or less (metastable approximations). By extrapolation accurate estimates can be derived of the Curie point and critical values of the energy and entropy. It is found that there is a marked difference in behaviour between two- and three-dimensional lattices, a far larger proportion of the entropy change taking place in the temperature region below the Curie point in the latter case. The corresponding specific heat curves are therefore much closer to those observed experimentally. Finally, a brief discussion is given of the dependence of the specific heat curve on lattice structure.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.