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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)

Abstract

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,
$$H = \mathop \Sigma \limits_{\alpha \in \Lambda } \Sigma \left( {{J_x}S_\alpha ^xS_{\alpha + \delta }^x + {J_y}S_\alpha ^yS_{\alpha + \delta }^y + {J_z}S_\alpha ^zS_{\alpha + \delta }^z} \right),\left( {{J_x},{J_y},{J_z}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ >} } 0} \right)$$
(1)
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.

Keywords

Thermodynamic Limit Parameter Region Hexagonal Lattice Present Contribution Spin Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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