 Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models by N. D. Mermin and H. Wagner

Physical Review Letters 17, 1133 (1966), DOI 10.1103/PhysRevLett.17.1133. The abstract states the absence of ferromagnetic or antiferromagnetic order at nonzero temperature in finite-range one- or two-dimensional isotropic spin-$S$ Heisenberg models. This is a primary source for the low-dimensional limitation of mean-field magnetic ordering.