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Quantum theory of one- and two-dimensional ferro- and antiferromagnets with an easy magnetization plane . I. ideal 1-d or 2-d lattices without in-plane anisotropy
Open accessAbstract
A « semi-polar » representation of the spin operators is introduced, which makes possible, in the harmonic approximation, the definition of magnons for any wavelength at low temperature in one-dimensional (= 1-D) or two-dimensional (= 2-D) magnetic systems without long-range order, provided they are of the « planar » type, i. e. they have an easy magnetization plane. The semi-polar representation is used to calculate the spin pair correlation function at low temperature. Its space-time Fourier transform (directly observable by neutron scattering) consists of a relatively broad peak due to spin fluctuations inside the easy plane, plus a narrower peak due to out-of-plane fluctuations. The intensity, width and lineshape of both peaks are calculated in both 1-D and 2-D cases for all momentum transfers, as well as the frequency shift as a function of temperature.
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Cites
Mermin, N. D., & Wagner, H. (1966) · Physical Review Letters · doi:10.1103/physrevlett.17.1133 · Cited by 8,363
Two soluble models of an antiferromagnetic chain
Lieb, E., Schultz, T., & Mattis, D. (1961) · Annals of Physics · doi:10.1016/0003-4916(61)90115-4 · Cited by 4,280
A Continued-Fraction Representation of the Time-Correlation Functions
Mori, H. (1965) · Progress of Theoretical Physics · doi:10.1143/ptp.34.399 · Cited by 1,799
General Theory of Spin-Wave Interactions
Dyson, F. J. (1956) · Physical Review · doi:10.1103/physrev.102.1217 · Cited by 1,627
Tables of Integrals and Other Mathematical Data.
Dwight, H. B. (1963) · Biometrika · doi:10.2307/2333782 · Cited by 921
Possibility of a Phase Transition for the Two-Dimensional Heisenberg Model
Stanley, H. E., & Kaplan, T. A. (1966) · Physical Review Letters · doi:10.1103/physrevlett.17.913 · Cited by 440
Cited by
Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin quantum number
Schulz, H. J. (1986) · Physical Review B · doi:10.1103/physrevb.34.6372 · Cited by 536
Colloquium: Spontaneous magnon decays
Zhitomirsky, M. E., & Chernyshev, A. L. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.219 · Cited by 278
Spectral-gap analysis for efficient tunneling in quantum adiabatic optimization
Brady, L. T., & van Dam, W. (2016) · Physical Review A · doi:10.1103/physreva.94.032309 · Cited by 17
Metadata
- Authors
- Villain, J.
- Venue
- Journal de Physique
- Publisher
- EDP Sciences
- Published
- 1974
- Volume
- 35
- Issue
- 1
- Pages
- 27-47
- ISSN
- 0302-0738 (ISSN-L)
- OpenAlex
- W2060067958
- Cited by
- 310
- References
- 6
- FWCI
- 7.85
- Type
- journal article
- Language
- en
- Open access
- green
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- Villain, J. (1974). Quantum theory of one- and two-dimensional ferro- and antiferromagnets with an easy magnetization plane . I. ideal 1-d or 2-d lattices without in-plane anisotropy. Journal de Physique. https://doi.org/10.1051/jphys%3A0197400350102700
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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