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

作者：N. David Mermin, Hermann‐Josef Wagner · 发表于：Physical Review Letters · 年份：1966 · DOI：10.1103/physrevlett.17.1133 · 被引用次数：8372 · 研究领域：Theoretical and Computational Physics、Stochastic processes and statistical mechanics、Complex Systems and Time Series Analysis

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.