
SIGMA 4 (2008), 007, 14 pages arXiv:0801.2780
http://dx.doi.org/10.3842/SIGMA.2008.007
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics
Three Order Parameters in Quantum XZ SpinOscillator Models with Gibbsian Ground States
Teunis C. Dorlas ^{a} and Wolodymyr I. Skrypnik ^{b}
^{a)} Dublin Institute for Advanced Studies, School of
Theoretical Physics, 10 Burlington Road, Dublin 4, Ireland
^{b)} Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine
Received October 29, 2007, in final form January 08, 2008; Published online January 17, 2008
Sections 1 and 2 have been rewritten, the main result and the proof have not been changed February 18, 2008.
Abstract
Quantum models on the hypercubic ddimensional lattice of
spin1/2 particles interacting with linear oscillators are
shown to have three ferromagnetic ground state order parameters. Two
order parameters coincide with the magnetization in the first and
third directions and the third one is a magnetization in a
continuous oscillator variable. The proofs use a generalized Peierls
argument and two Griffiths inequalities. The class of
spinoscillator Hamiltonians considered manifest maximal ordering in
their ground states. The models have relevance for hydrogenbond
ferroelectrics. The simplest of these is proven to have a unique
Gibbsian ground state.
Key words:
order parameters; spinboson model; Gibbsian ground state.
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