  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.
