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Some generalized order-disorder transformations

Published online by Cambridge University Press:  24 October 2008

R. B. Potts
R. B. Potts
Affiliation:
The Clarendon LaboratoryOxford*
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Extract

In considering the statistics of the ‘no-field’ square Ising lattice in which each unit is capable of two configurations and only nearest neighbours interact, Kramers and Wannier (3) were able to deduce an inversion transformation under which the partition function of the lattice is invariant when the temperature is transformed from a low to a high (‘inverted’) value. The important property of this inversion transformation is that its fixed point gives the transition point of the lattice.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 1 , January 1952 , pp. 106 - 109
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Ashkin, J. and Teller, E.Phys. Rev. (2), 64 (1943), 178.CrossRefGoogle Scholar
(2)Domb, C.Proc. roy. Soc. A, 196 (1949), 36.Google Scholar
(3)Kramers, H. A. and Wannier, G. H.Phys. Rev. (2), 60 (1941), 252, 263.CrossRefGoogle Scholar
(4)Potts, R. B. D.Phil, thesis, University of Oxford (1951).Google Scholar
(5)Wannier, G. H.Rev. mod. Phys. 17 (1945), 50.CrossRefGoogle Scholar