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2004

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Reviews of topical problems


Convergence problems of Coulomb and multipole sums in crystals


A.V. Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, prosp. akad. Lavrenteva 3, Novosibirsk, 630090, Russian Federation

Different ways of calculating Coulomb and dipole sums over crystal lattices are analyzed comparatively. It is shown that the currently alleged disagreement between various approaches originates in ignoring the requirement for the self-consistency of surface conditions, which are of fundamental importance due to the long-range nature of the bulk interactions that these sums describe. This is especially true of surfaces arising when direct sums for infinite translation-invariant structures are truncated. The charge conditions for actual surfaces being self-consistently adjusted to the bulk state are formally the same as those on the truncation surface, consistent with the concept of the thermodynamic limit for the bulk-state absolute equilibrium and with the fact that the surface energy contribution in this case is, naturally, statistically small compared to the bulk contribution. Two-point multipole expansions are briefly discussed, and the problems associated with the boundary of their convergence circle are pointed out.

Fulltext pdf (436 KB)
Fulltext is also available at DOI: 10.1070/PU2004v047n10ABEH001720
PACS: 41.20.Cv, 61.50.Lt, 75.10.−b, 81.40.Rs (all)
DOI: 10.1070/PU2004v047n10ABEH001720
URL: https://ufn.ru/en/articles/2004/10/a/
000226730200001
2004PhyU...47..965K
Citation: Kholopov E V "Convergence problems of Coulomb and multipole sums in crystals" Phys. Usp. 47 965–990 (2004)
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Оригинал: Холопов Е В «Проблемы сходимости кулоновских и мультипольных сумм в кристаллах» УФН 174 1033–1060 (2004); DOI: 10.3367/UFNr.0174.200410a.1033

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  1. V.B. Shikin “Instability and reconstruction of a charged liquid surface54 1203–1225 (2011)
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  3. V.D. Buchel’nikov, N.K. Dan’shin et alOn the relative contributions of precessional and longitudinal oscillations to the dynamics of magnets42 957–990 (1999)
  4. P.A. Alekseev “Neutron spectroscopy and strongly correlated electrons: a view from the inside60 58–90 (2017)
  5. V.G. Bar’yakhtar, A.N. Bogdanov, D.A. Yablonskii “The physics of magnetic domains31 810–835 (1988)
  6. A.A. Katanin, V.Yu. Irkhin “Magnetic order and spin fluctuations in low-dimensional insulating systems50 613–635 (2007)
  7. Yu.A. Izyumov, Yu.N. Skryabin “Double exchange model and the unique properties of the manganites44 109–134 (2001)
  8. Yu.A. Izyumov, E.Z. Kurmaev “Materials with strong electron correlations51 23–56 (2008)
  9. I.S. Lyubutin, A.G. Gavriliuk “Research on phase transformations in 3d-metal oxides at high and ultrahigh pressure: state of the art52 989–1017 (2009)
  10. A.S. Andreenko, S.A. Nikitin “Magnetic properties of amorphous rare-earth — 3d-transition-metal alloys40 581–597 (1997)
  11. V.S. Dotsenko “Physics of the spin-glass state36 (6) 455–485 (1993)
  12. E.Z. Valiev “Phenomenological theory of magnetoelastic interactions in Invars and Elinvars34 (8) 685–704 (1991)
  13. M.I. Kaganov, A.V. Chubukov “Interacting magnons30 1015–1040 (1987)
  14. A.A. Pervishko, D.I. Yudin “Microscopic approach to the description of spin torques in two-dimensional Rashba ferromagnets and antiferromagnets65 215–226 (2022)
  15. E.A. Turov, V.G. Shavrov “Broken symmetry and magnetoacoustic effects in ferroand antiferromagnetics26 593–611 (1983)
  16. A.F. Andreev, V.I. Marchenko “Symmetry and the macroscopic dynamics of magnetic materials23 21–34 (1980)
  17. I.Ya. Korenblit, E.F. Shender “Ferromagnetism of disordered systems21 832–851 (1978)
  18. N.P. Grazhdankina “Magnetic first order phase transitions11 727–745 (1969)
  19. G.R. Khutsishvili “Spin diffusion8 743–769 (1966)
  20. V.S. Kogan “Isotope effects in the structural properties of solids5 951–975 (1963)

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