Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States

Details Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States

2008-01-17

arxiv.org/abs/0801.2780v2

SIGMA 4 (2008), 007, 14 pages

Physics

Condensed Matter

Statistical Mechanics

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'', pu

Scientific paper

10.3842/SIGMA.2008.007

Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 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 spin-oscillator Hamiltonians considered manifest maximal ordering in their ground states. The models have relevance for hydrogen-bond ferroelectrics. The simplest of these is proven to have a unique Gibbsian ground state.

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