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

@article{Mermin1966AbsenceOF,
  title={Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models},
  author={N. David Mermin and Herbert Wagner},
  journal={Physical Review Letters},
  year={1966},
  volume={17},
  pages={1133-1136}
}
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. 
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ZusammenfassungBeim Austauschvorgang der Elektronen im Kristall werden die Eigenfunktionen nullter und Eigenwerte erster Näherung für die Termsysteme hoher Multiplizität bestimmt, wobei die Kopplung