SIGMA 2 (2006), 011, 6 pages math-ph/0601060
Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States
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
A class of general spin 1/2 lattice models on
hyper-cubic lattice Zd, whose Hamiltonians are sums of two
functions depending on the Pauli matrices S1, S2 and S3,
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
Gibbsian eigen (ground) states; quantum spin models.
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