抄録
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 Δ satisfies 0≤Δ<0.20 or Δ>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≤Δ≤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 (Δ≥1). The XXZ model on the two-dimensional hexagonal lattice is proved to have finite ground-state long-range order for any value of Δ(≥0) if S≥1 and for Δ>2.55 when S=1⁄2.
