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January 1, 1952Mathematical Proceedings of the Cambridge Philosophical Society2,149 citations

Some generalized order-disorder transformations

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RPR. B. Potts

Key Points

  • Investigate generalized order-disorder transformations and the invariance properties of partition functions in statistical lattice models.
  • Analyzed statistical mechanics of the two-dimensional, no-field square Ising model featuring two-state units and nearest-neighbor interactions.
  • Applied Kramers-Wannier temperature inversion transformations mapping low-temperature states to high-temperature states.
  • Demonstrated that the lattice partition function remains invariant under dual temperature inversion.
  • Identified that the fixed point of the inversion transformation precisely locates the critical order-disorder transition temperature.

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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Cite This Study

R. B. Potts (1952) studied this question.

synapsesocial.com/papers/6a0efefd1c5e2d2319fa35b1https://doi.org/10.1017/s0305004100027419
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