Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
Abstract
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.
Cite
@article{arxiv.0801.2780,
title = {Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States},
author = {Teunis C. Dorlas and Wolodymyr I. Skrypnik},
journal= {arXiv preprint arXiv:0801.2780},
year = {2008}
}
Comments
This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'', published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ v2: sections 1 and 2 have been rewritten, the main result and the proof have not been changed