The Spherical Model of a Ferromagnet

Phys. Rev. 86, 821 – Published 15 June 1952
T. H. Berlin and M. Kac


A mathematical model, the spherical model, of a ferromagnet is described. The model is a generalization of the Ising model; and one-, two-, and three-dimensional lattices of infinite extent can be extensively discussed. A three-dimensional lattice shows ferromagnetic behavior and provides a statistical model of the Weiss phenomenological theory. The limiting free energy appears in a form which contains two of the essential features of the exactly known Ising model results in one and two dimensions. This suggests the probable form of the limiting free energy for the three-dimensional Ising model. A simplified model, the Gaussian model, is briefly discussed because this model also contains some of the significant features of the Ising model. However, the Gaussian model, unlike the spherical model, is not defined for all temperatures.


  • Received 28 February 1952
  • Published in the issue dated June 1952

© 1952 The American Physical Society

Authors & Affiliations

T. H. Berlin

  • Department of Physics, The Johns Hopkins University, Baltimore, Maryland

M. Kac

  • Department of Mathematics, Cornell University, Ithaca, New York

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