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Some generalized order-disorder transformations

  • R. B. Potts (a1)

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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.

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(1)Ashkin, J. and Teller, E.Phys. Rev. (2), 64 (1943), 178.
(2)Domb, C.Proc. roy. Soc. A, 196 (1949), 36.
(3)Kramers, H. A. and Wannier, G. H.Phys. Rev. (2), 60 (1941), 252, 263.
(4)Potts, R. B. D.Phil, thesis, University of Oxford (1951).
(5)Wannier, G. H.Rev. mod. Phys. 17 (1945), 50.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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