Mathematical Proceedings of the Cambridge Philosophical Society · 1952 · 2.1K citations · 4 references
Natural SciencesPhysicsCondensed Matter PhysicsSolid State PhysicsThermodynamicsCrystal LatticeDisordered SystemsOrder-disorder ThermodynamicsOrder-disorder TransformationsOrdering TransformationsPhase TransitionsDisorderDisorder-to-order TransformationFixed-point CharacterizationIsing ModelLattice ModelsOrder-disorder Phase DiagramOrder-disorder Phase TransitionPartition Function
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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Statistics of the Two-Dimensional Ferromagnet. Part I
H. A. Kramers, Gregory H. Wannier · Physical Review · 1941 · 1.8K citations
Statistics of Two-Dimensional Lattices with Four Components
J. Ashkin, Edward Teller · Physical Review · 1943 · 654 citations