articleTop 1% cited
Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
Physical Review Letters · 1966 · Vol. 17(22) · pp. 1133–1136
N. David Mermin✉(Cornell University)Hermann‐Josef Wagner(Cornell University)
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.
Theoretical and Computational PhysicsStochastic processes and statistical mechanicsComplex Systems and Time Series AnalysisAntiferromagnetismFerromagnetismIsotropyHeisenberg modelCondensed matter physicsPhysicsSpin (aerodynamics)Exchange interactionVariety (cybernetics)Quantum mechanics
Citations
8,024
FWCI
15.68
field-weighted impact
References
9
Percentile
100%
vs. same field & year
Citations per year
Cited by
Collective motion
Physics Reports · 2012 · 2,838 citations
There are no Goldstone bosons in two dimensions
Communications in Mathematical Physics · 1973 · 1,318 citations
Strong anisotropy and magnetostriction in the two-dimensional Stoner ferromagnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Fe</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>GeTe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Physical review. B./Physical review. B · 2016 · 412 citations
Flocks, herds, and schools: A quantitative theory of flocking
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1998 · 1,567 citations
The quadratic-layer antiferromagnet
Journal of Physics and Chemistry of Solids · 1970 · 450 citations
Strain-tunable magnetic anisotropy in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CrCl</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CrBr</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CrI</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>
Physical review. B./Physical review. B · 2018 · 609 citations
Renormalisation group analysis of the phase transition in the 2D Coulomb gas, Sine-Gordon theory and XY-model
Journal of Physics A Mathematical and General · 1980 · 361 citations
Electronic properties of disordered two-dimensional carbon
Physical Review B · 2006 · 1,425 citations
References
Zur Theorie des Ferromagnetismus
The European Physical Journal A · 1930 · 1,133 citations
Citation Network
How this paper connects to the literature. Drag to explore, click any node to open that paper.