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Theory of invariant transformations of the Ising lattice


Operators of creation and annihilation of atoms in the Ising lattice that conserve the partition function are considered. A change in the geometrical and topological characteristics of the lattice may be accompanied by the replacement of many-particle interactions in the lattice by two-particle interactions and vice versa. The construction of the operators makes essential use of the theory of characters.

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Literature cited

  1. 1.

    E. Montroll, “Lectures on the Ising model,” in: Stability and Phase Transitions [Russian translations], Mir, Moscow (1973).

  2. 2.

    L. S. Pontyagin, Topological Groups, New York (1966) (The reference is to p.250 of the later Russian edition published by Nauka in 1973).

  3. 3.

    C. Domb, “The Ising model,” in: C. Domb and M. S. Green, Phase Transitions and Critical Phenomena, Academic Press, New York, p. 433.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 5–11, November, 1980.

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Men', B.A. Theory of invariant transformations of the Ising lattice. Soviet Physics Journal 23, 915–920 (1980).

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  • Partition Function
  • Topological Characteristic
  • Invariant Transformation
  • Ising Lattice