ISSN:
1572-9613
Keywords:
Long-range order
;
quantum effects
;
anisotropy
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ〈0.29 (XY-like) orΔ〉1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ〈0.032 (XY-like) or 0.67〈Δ〈1.34 (almost isotropic) orΔ〉1.80 (Ising-like) ifS=1;Δ〉1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01042599
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