Teunis C. Dorlas, Wolodymyr I. Skrypnik, “Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States”, SIGMA, 2008, Volume 4,007, 14 pp.

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

Teunis C. Dorlas^a, 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

Abstract: Quantum models on the hyper-cubic $d$-dimensional lattice of spin-$\frac12$ 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.

Keywords: order parameters; spin-boson model; Gibbsian ground state.

MSC: 82B10; 82B20; 82B26

Received: October 29, 2007; in final form January 8, 2008; Published online January 17, 2008

Language: English

DOI: 10.3842/SIGMA.2008.007