Mermin and Wagner: absence of magnetic order in low-dimensional isotropic Heisenberg models

What changed

Proved absence of ferromagnetic and antiferromagnetic order in specified one- and two-dimensional isotropic Heisenberg models.

Scientific scope

The record is the exact two-author 1966 letter together with its published erratum boundary. The theorem depends on dimensionality, symmetry and interaction assumptions; it does not forbid all phase transitions or all order in low-dimensional systems.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact two-author 1966 letter together with its published erratum boundary. The theorem depends on dimensionality, symmetry and interaction assumptions; it does not forbid all phase transitions or all order in low-dimensional systems.

Contributors

• N. D. Mermin · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.
• H. Wagner · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• APS page for Mermin-Wagner paper
• APS full text of Mermin-Wagner paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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