The spin 1/2 XXZ model for Δ<-1

Michio Jimbo, Kei Miki, Tetsuji Miwa +1 more

Yu. G. Stroganov

Yukiyasu Ozeki, Hidetoshi Nishimori, Yasuhiro Tomita

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.

Minoru Takahashi

An Du, G.Z. Wei

The double-layer antiferromagnetic quantum XXZ model is studied by the bond-operator mean-field theory. The transverse and longitudinal modes in excited spectra, and the phase diagram for disorder–order phase transition about Δ and J/J⟂, which are the relative strength of spin anisotropy and the ratio of the intralayer coupling to the interlayer coupling, respectively, are obtained. It is found that the critical ratio of (J/J⟂)c is 0.174 for XY model (Δ = 0), and is 0.430 for isotropic model (Δ = 1). In the disordered phase and on the critical points, the excitation spectra are analyzed. The spin gap from the condensed spin singlets to the first excited states, the ground state energy and the spin wave velocities in the disordered state are calculated as functions of parameters Δ and J/J⟂.

Holger Fehske, C. Schindelin, Alexander Weiße +2 more

Ground-state and thermodynamic properties of the spin-1/2 two-dimensional easy-plane XXZ model are investigated by both a Green's-function approach and by Lanczos diagonalization on lattices with up to 36 sites. We calculate the spatial and temperature dependences of various spin correlation functions, as well as the wave-vector dependence of the spin susceptibility for all anisotropy parameters delta. In the easy plane ferromagnetic region (-1 < delta < 0), the longitudinal correlators of spins at distance r change sign at a nite temperature T0 (delta, r). This transition, observed in the 2D case for the first time, can be interpreted as a quantum to classical crossover.