Geodesic
Order Parameters in XXZ-Type Spin $\frac12$ Quantum Models with Gibbsian Ground States
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A class of general spin $\frac12$ lattice models on hyper-cubic 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 $\alpha$ playing the role of the inverse temperature. It is shown that the ferromagnetic order in $x$ direction exists for all dimensions $d\geq 1$ for a wide class of considered models (a proof is remarkably simple).
Keywords: Gibbsian eigen (ground) states; quantum spin models. 
@article{SIGMA_2006_2_a10,
     author = {Wolodymyr Skripnik},
     title = {Order {Parameters} in {XXZ-Type} {Spin} $\frac12$ {Quantum} {Models} with {Gibbsian} {Ground} {States}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2006},
     volume = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a10/}
}
TY  - JOUR
AU  - Wolodymyr Skripnik
TI  - Order Parameters in XXZ-Type Spin $\frac12$ Quantum Models with Gibbsian Ground States
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2006
VL  - 2
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a10/
LA  - en
ID  - SIGMA_2006_2_a10
ER  - 
%0 Journal Article
%A Wolodymyr Skripnik
%T Order Parameters in XXZ-Type Spin $\frac12$ Quantum Models with Gibbsian Ground States
%J Symmetry, integrability and geometry: methods and applications
%D 2006
%V 2
%U http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a10/
%G en
%F SIGMA_2006_2_a10
Wolodymyr Skripnik. Order Parameters in XXZ-Type Spin $\frac12$ Quantum Models with Gibbsian Ground States. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a10/

[1] Dorlas T., Skrypnik W., “Two order parameters in quantum XZ spin midels with Gibbsian ground states”, J. Phys. A: Math. Gen., 37 (2004), 6623–6632 | DOI | MR | Zbl

[2] Kirkwood J., Thomas L., “Expansions and phase transitions for the ground state of quantum Ising lattice systems”, Comm. Math. Phys., 88 (1983), 569–580 | DOI | MR

[3] Matsui T., “A link between quantum and classical Potts models”, J. Statist. Phys., 59 (1990), 781–798 | DOI | MR | Zbl

[4] Matsui T., “Uniqueness of translation invariant ground state in quantum spin systems”, Comm. Math. Phys., 126 (1990), 453–467 | DOI | MR | Zbl

[5] Alcaraz F., “Exact steady states of asymmetric diffusion and two-species annihilation with back reaction from the ground state of quantum spin model”, Internat. J. Modern Phys., 25–26 (1994) ; 3449–3461 | MR | MR

[6] Alcaraz F., Salinas S., Wrechinsky W., “Anisotropic quantum domains”, Phys. Rev. Lett., 5 (1995), 930–933 | DOI

[7] Matsui T., “On ground state degeneracy of $Z_2$ symmetric quantum spin models”, Publ. Res. Inst. Math. Sci., 27 (1991), 658–679 | DOI | MR

[8] Thomas L., Yin Z., “Low temperature expansions for the Gibbs states of quantum Ising lattice systems”, J. Math. Phys., 10 (1984), 3128–3134 | DOI | MR