## Abstract

The existence of long-range order is proved under certain conditions for the antiferromagnetic XYZ model on the simple cubic or the square lattice. In particular, the spin-1/2 XXZ model on the square lattice is shown to have ground-state long-range order if the exchange anisotropy ∆ satisfies 0≦∆< <0.20 or ∆ > 1.72, which improves the result of Kubo and Kishi. The existence of long-range order of the z-component of the spin operator is proved for the XXZ model with XY-like anisotropy (0 ≦ ∆ ≦ 1) under certain conditions. A similar result is shown to hold for the long-range order in the x-direction for the Ising-like model (∆ ≧ 1). The XXZ model on the two-dimensional hexagonal lattice is proved to have finite ground-state long-range order for any value of ∆(≧0) if S ≧ l and for ∆ ?2.55 when S=1/2.

Original language | English |
---|---|

Pages (from-to) | 82-90 |

Number of pages | 9 |

Journal | journal of the physical society of japan |

Volume | 58 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1989 Jan 1 |

Externally published | Yes |

## ASJC Scopus subject areas

- Physics and Astronomy(all)