Ground-State Long-Range Order of the Two-Dimensional Quantum Antiferromagnet

  • Y. Ozeki
  • H. Nishimori
  • Y. Tomita
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 43)


The two-dimensional quantum antiferromagnet is of active current interest. One of the main unsettled problems is whether magnetic long-range order exists or not in the ground state of the quantum antiferromagnet on the square lattice. In the present contribution we treat the XYZ model,
$$H = \mathop \Sigma \limits_{\alpha \in \Lambda } \Sigma \left( {{J_x}S_\alpha ^xS_{\alpha + \delta }^x + {J_y}S_\alpha ^yS_{\alpha + \delta }^y + {J_z}S_\alpha ^zS_{\alpha + \delta }^z} \right),\left( {{J_x},{J_y},{J_z}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ >} } 0} \right)$$
and derive the parameter region in which long-range order certainly exists. We also show that long-range order along the non-principal axis (e.g. z-axis in the XY-like region) exists in the XXZ model (J x =J y =1, J z =Δ)under certain conditions.


Thermodynamic Limit Parameter Region Hexagonal Lattice Present Contribution Spin Component 
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  1. 1.
    F.J. Dyson, E.H. Lieb, B. Simon: J. Stat. Phys. 18, 335 (1978)CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    E.J. Neves, J.F. Perez: Phys. Lett. 114A, 331 (1986)CrossRefGoogle Scholar
  3. 3.
    I. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki: Commun. Math. Phys. 115, 477 (1988)CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    K. Kubo: Phys. Rev. Lett. 61, 110 (1988)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    H. Nishimori, K. Kubo, Y. Ozeki, Y. Tornita, T. Kishi: preprintGoogle Scholar
  6. 6.
    T. Kennedy, E.H. Lieb, B.S. Shastry: preprintGoogle Scholar
  7. 7.
    K. Kubo, T. Kishi: preprintGoogle Scholar
  8. 8.
    Y. Ozeki, H. Nishimori, Y. Tornita: preprintGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • Y. Ozeki
    • 1
  • H. Nishimori
    • 1
  • Y. Tomita
    • 1
  1. 1.Department of PhysicsTokyo Institute of TechnologyMeguro-ku, TokyoJapan

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