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On Ising's model of ferromagnetism

  • R. Peierls
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Ising discussed the following model of a ferromagnetic body: Assume N elementary magnets of moment μ to be arranged in a regular lattice; each of them is supposed to have only two possible orientations, which we call positive and negative. Assume further that there is an interaction energy U for each pair of neighbouring magnets of opposite direction. Further, there is an external magnetic field of magnitude H such as to produce an additional energy of − μH (+ μH) for each magnet with positive (negative) direction.

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* Ising, , Zeits. für Physik, 31 (1925), 253.

Heisenberg, W., Zeits. für Physik, 49 (1928), 619; for an account of the theory of Heisenberg and the extensions by Bloch and others, see Bloch, F., Handbuch der Radiologie, vi, 2 (Leipzig, 1934), 375.

* Bragg, W. L. and Williams, E. J., Proc. Roy. Soc. A. 145 (1934), 699; Borelius, , Ann. d. Physik, 20 (1934), 57; Fowler, R. H., Proc. Roy. Soc. A. 149 (1935), 1; Bethe, H. A., Proc. Roy. Soc. A. 150 (1935), 552.

Cf. the preceding paper. This will be referred to as A.

* This value could be considerably improved without difficulty. Taking into account that according to condition (2) two successive steps must never be opposite to each other, there is only a choice of three possibilities for all but the first step, and in this way we easily obtain ⅓ instead of ¼.

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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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