
SIGMA 2 (2006), 011, 6 pages mathph/0601060
https://doi.org/10.3842/SIGMA.2006.011
Order Parameters in XXZType Spin 1/2 Quantum Models with Gibbsian Ground States
Wolodymyr Skrypnik
Institute of Mathematics, 3 Tereshchenkivs'ka Str., Kyiv 4, 01601 Ukraine
Received October 19, 2005, in final form January 16, 2006; Published online January 24, 2006
Abstract
A class of general spin 1/2 lattice models on
hypercubic lattice Z^{d}, whose Hamiltonians are sums of two
functions depending on the Pauli matrices S^{1}, S^{2} and S^{3},
respectively, are found, which have Gibbsian eigen (ground) states
and two order parameters for two spin components x, z
simultaneously for large values of the parameter α playing
the role of the inverse temperature. It is shown that the
ferromagnetic order in x direction exists for all dimensions
d ≥ 1 for a wide class of considered models (a proof is
remarkably simple).
Key words:
Gibbsian eigen (ground) states; quantum spin models.
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