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The cooperative behaviour of a two-dimensional defect crystal

Published online by Cambridge University Press:  24 October 2008

E. W. Elcock
E. W. Elcock
Affiliation:
Natural Philosophy DepartmentMarischal CollegeAberdeen
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Abstract

The Ising model of a two-dimensional ferromagnetic crystal containing defects is considered. It is shown that the combinatorial method is particularly appropriate to the investigation of the two-dimensional defect crystal and how it may be readily modified to calculate the partition function for such a crystal. It is found that the cooperative behaviour of the infinite perfect crystal, as indicated by the occurrence of a logarithmic singularity in the specific heat as a function of temperature, is not destroyed in the defect crystal; the singularity persists, though at a progressively lower temperature as the density of defects is increased, until a high density of defects is reached. The value of this limiting density of defects, above which the cooperative behaviour is destroyed, is calculated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 4 , October 1957 , pp. 863 - 869
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

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