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High-temperature dynamics of the anisotropic spin-1/2 square lattice Heisenberg model studied by moment methods

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Zeitschrift für Physik B Condensed Matter

Abstract

The spin dynamics of the anisotropic spin-1/2 nearest-neighbour Heisenberg model (XYZ model) on a plane square lattice is studied at infinite temperature. Low-order coefficients of the short-time expansions for spin-spin correlation functions are calculated. The necessary commutator algebra may be performed by a computer. The series obtained for the spin correlation function are the longest ones available up to now. The series coefficients are used to construct rigorous upper and lower bounds to autocorrelation functions and near-neighbour correlation functions.

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References

  1. Steiner, M., Villain, J., Windsor, C.G.: Adv. Phys.25, 87 (1976)

    Google Scholar 

  2. Schneider, T, Stoll, E.: In: Solitons. Trullinger, S.E., Zakharov, V.E., Pokrovsky, V.L. (eds.), p. 129. Amsterdam: Elsevier Science Publishers 1986

    Google Scholar 

  3. Müller, G.: Phys. Rev. Lett.60, 2785 (1988) is a recent contribution to this discussion; compare Gerling, R.W., Landau, D.P. (submitted for publication) for a computer simulation leading to a different conclusion

    Google Scholar 

  4. See[2] and the references quoted there; a more recent example is Müller, G.: Z. Phys. B — Condensed Matter68, 149 (1987)

    Google Scholar 

  5. Platz, O., Gordon, R.G.: Phys. Rev. Lett.30, 264 (1973). For an early application to spin correlation functions see also: Platz, O., Gordon, R.G.: Phys. Rev. B7, 4764 (1973)

    Google Scholar 

  6. Roldan, J.M.R., McCoy, B.M., Perk, J.H.H.: Physica136 A, 255 (1986)

    Google Scholar 

  7. Brandt, U., Stolze, J.: Z. Phys. B-Condensed Matter64, 327 (1986)

    Google Scholar 

  8. Morita, T.: J. Math. Phys.12, 2062 (1971). In this reference, the momentsM 2lz (r) were calculated for a uniaxial (J x=Jy) Heisenberg model in one dimension (l≦5) and on square and simple cubic lattices (l≦4)

    Google Scholar 

  9. Sur, A., Jasnow, D., Lowe, I.J.: Phys. Rev. B12, 3845 (1975)

    Google Scholar 

  10. Brandt, U., Jacoby, K.: Z. Phys. B25, 181 (1976)

    Google Scholar 

  11. Capel, H.W., Perk, J.H.H.: Physica87 A, 211 (1977)

    Google Scholar 

  12. Niemeijer, Th.: Physica36, 377 (1967);

    Google Scholar 

  13. Katsura, S., Horiguchi, T., Suzuki, M.: Physica46, 67 (1970); or see Section III of [6]

    Google Scholar 

  14. Mead, L.R., Papanicolaou, N.: J. Math. Phys.25, 2404 (1984)

    Google Scholar 

  15. Fedders, P.A., Carlsson, A.E.: Phys. Rev. B32, 229 (1985)

    Google Scholar 

  16. Zhang, Y.-M., Tu, J.-M.: Z. Phys. B-Condensed Matter74, 329 (1989)

    Google Scholar 

  17. Krein, M.G.: Am. Math. Soc. Transl. Ser. 2,12, 1 (1959)

    Google Scholar 

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Stolze, J., Brandt, U. High-temperature dynamics of the anisotropic spin-1/2 square lattice Heisenberg model studied by moment methods. Z. Physik B - Condensed Matter 77, 111–118 (1989). https://doi.org/10.1007/BF01313627

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  • DOI: https://doi.org/10.1007/BF01313627

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