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

1966/11/28 by N. David Mermin, Hermann‐Josef Wagner · 15 citations
Physics and Astronomy · Mathematics · Economics, Econometrics and Finance · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Complex Systems and Time Series Analysis #Antiferromagnetism #Ferromagnetism #Isotropy #Heisenberg model #Condensed matter physics #Physics #Spin (aerodynamics) #Exchange interaction #Variety (cybernetics) #Quantum mechanics #Mathematics #Thermodynamics

paper · doi:10.1103/physrevlett.17.1133

openalex publication_date 1966/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• On Ising's model of ferromagnetism

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• Mermin–Wagner theorem [wikipedia]