Dynamic Scaling in the Two-Dimensional Heisenberg Antiferromagnet

  • Gary M. Wysin
  • Alan R. Bishop
Part of the NATO ASI Series book series (NSSB, volume 264)


The two-dimensional Heisenberg antiferromagnet has generated considerable interest with respect to its applications for understanding copper-oxide -based high temperature superconductors.1 The model is described by a Hamiltonian,
$$H = J\sum\limits_{\left( {n,m} \right)} {{{\vec S}_n}{{\vec S}_m}}$$
where J > 0 and the sum is over nearest neighbor spin variables Sn. While analytic calculations of either ground state or dynamic properties are very difficult for this and related nonlinear spin models, it is sometimes possible to extract important information from numerical calculations. Some success in obtaining ground state properties for the spin-1/2 model has resulted from quantum Monte Carlo calculations.2 However, the principle interest here is in dynamics, for which quantum Monte Carlo calculations are emerging but not yet well-developed. Nevertheless, progress in obtaining quantities such as the dynamic structure function S(q,ω) is occuring.3


Correlation Length Scaling Function Rotor Model Ground State Property Nonlinear Sigma Model 
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  1. 1.
    S. Chakravarty, in “HTC: The Los Alamos Meeting,” K. Bedell, D. Pines and J.R. Schrieffer, ed., Addison-Wesley, Redwood, CA (1990).Google Scholar
  2. 2.
    H.-Q. Ding and M.S. Makivic’, Phys. Rev. Lett. 64:1449 (1990);ADSCrossRefGoogle Scholar
  3. 2a.
    J.D. Reger and A.P. Young, Phys. Rev. B37:5978 (1988).ADSGoogle Scholar
  4. 3.
    S.R. White, D.J. Scalapino, R.L. Sugar and N.E. Bickers, Phys. Rev. Lett. 63:1523 (1989);ADSCrossRefGoogle Scholar
  5. 3a.
    M. Jarrell and O. Biham, Phys. Rev. Lett. 63:2504 (1989).ADSCrossRefGoogle Scholar
  6. 4.
    S. Chakravarty, B.I. Halperin and D. Nelson, Phys. Rev. Lett. 39:2344 (1989).ADSGoogle Scholar
  7. 5.
    F.D.M. Haldane, Phys. Rev. Lett. 50:1153 (1983);MathSciNetADSCrossRefGoogle Scholar
  8. 5a.
    F.D.M. Haldane, Physics Letters 93A:464 (1983).MathSciNetADSGoogle Scholar
  9. 6.
    S. Tyc, B.I. Halperin and S. Chakravarty, Phys. Rev. Lett. 62:835 (1989).ADSCrossRefGoogle Scholar
  10. 7.
    G.M. Wysin and A.R. Bishop, Phys. Rev. B42:810 (1990).ADSGoogle Scholar
  11. 8.
    This form was suggested by calculations of G. Reiter (private communication). A product of Lorentzians also describes S(q,ω) for the 1-D XY model, as in Eq. 3.2 of D.R. Nelson and D.S. Fisher, Phys. Rev. B16:4945 (1977).MathSciNetADSGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Gary M. Wysin
    • 1
  • Alan R. Bishop
    • 2
  1. 1.Department of PhysicsKansas State UniversityManhattanUSA
  2. 2.Los Alamos National LaboratoryLos AlamosUSA

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