
SIGMA 2 (2006), 011, 6 pages mathph/0601060
http://dx.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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References
 Dorlas T., Skrypnik W., Two order parameters in quantum XZ spin
midels with Gibbsian ground states, J. Phys. A: Math. Gen.,
2004, V.37, 66236632.
 Kirkwood J., Thomas L., Expansions and phase transitions for the
ground state of quantum Ising lattice systems, Comm. Math.
Phys., 1983, V.88, 569580.
 Matsui T., A link between quantum and classical Potts models,
J. Statist. Phys., 1990, V.59, 781798.
 Matsui T., Uniqueness of translation invariant ground
state in quantum spin systems, Comm. Math. Phys., 1990,
V.126, 453467.
 Alcaraz F., Exact steady states of asymmetric diffusion and
twospecies annihilation with back reaction from the ground state
of quantum spin model, Internat. J. Modern Phys., 1994,
V.2526, 34493461.
 Alcaraz F., Salinas S., Wrechinsky W., Anisotropic quantum
domains, Phys. Rev. Lett., 1995, V.5, 930933.
 Matsui T., On ground state degeneracy of Z_{2}
symmetric quantum spin models, Publ. Res. Inst. Math. Sci.,
1991, V.27, 658679.
 Thomas L., Yin Z., Low temperature
expansions for the Gibbs states of quantum Ising lattice systems,
J. Math. Phys., 1984, V.10, 31283134.

