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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 48, Issue 1
  • January 1952, pp. 106-109

Some generalized order-disorder transformations

  • R. B. Potts (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100027419
  • Published online: 24 October 2008
Abstract

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)J. Ashkin and E. Teller Phys. Rev. (2), 64 (1943), 178.

(2)C. Domb Proc. roy. Soc. A, 196 (1949), 36.

(3)H. A. Kramers and G. H. Wannier Phys. Rev. (2), 60 (1941), 252, 263.

(5)G. H. Wannier Rev. mod. Phys. 17 (1945), 50.

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  • EISSN: 1469-8064
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