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Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models

Phys. Rev. Lett. 17, 1133 – Published 28 November 1966
N. D. Mermin and H. Wagner

Abstract

It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-S Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.

DOI: http://dx.doi.org/10.1103/PhysRevLett.17.1133

  • Received 17 October 1966
  • Published in the issue dated 28 November 1966

© 1966 The American Physical Society

Authors & Affiliations

N. D. Mermin* and H. Wagner

  • Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York

  • *Alfred P. Sloan Foundation Fellow.
  • Permanent address: Max-Planck Institute für Physik, München, Germany.

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