Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
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.
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The exact time at which the bandgap appears is difficult to identify, probably because there is no long-range order of iron spins on the surface and differently ordered domains contribute differently gapped signals.
“It is difficult to identify the exact time at which the bandgap appears, probably because there is no long-range order of iron spins on the surface 28,29 , and differently ordered domains will yield differently gapped contributions to the photoemission signal.”
From A topological insulator surface under strong Coulomb, magnetic and disorder perturbations (2011) · cites this paper as [28]
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“In the opposite limit, if g1 decays exponentially on a length scale much shorter than Lx, the integral in (1) is independent of Lx.”
BackgroundThe nonperturbative functional renormalization group and its applications
Dupuis, N., Canet, L., Eichhorn, A., Metzner, W., Pawlowski, J. M., Tissier, M., & Wschebor, N. (2021) · Physics Reports · doi:10.1016/j.physrep.2021.01.001 · Cited by 660 · see citing works
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Tranquada, J. M. (2020) · Advances in Physics · doi:10.1080/00018732.2021.1935698 · Cited by 84 · see citing works
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- Authors
- Mermin, N. D., & Wagner, H.
- Affiliations
- Cornell University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1966-11-28
- Volume
- 17
- Issue
- 22
- Pages
- 1133-1136
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2008317504
- Cited by
- 8,363
- References
- 9
- Citations by year
- 2026: 325 · 2025: 396 · 2024: 437 · 2023: 462 · 2022: 449 · 2021: 468 · 2020: 504 · 2019: 414 · 2018: 286 · 2017: 277 · 2016: 250 · 2015: 212 · 2014: 201 · 2013: 197 · 2012: 181
- FWCI
- 14.33
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- Heisenberg model, ferromagnetism, antiferromagnetism, spin chains, two-dimensional spin systems, spin ordering
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Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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