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

TL;DR

This paper demonstrates that certain quantum spin-oscillator models on hyper-cubic lattices exhibit three distinct ferromagnetic order parameters, with proofs utilizing generalized Peierls arguments and Griffiths inequalities, relevant to ferroelectric materials.

Contribution

It introduces a class of quantum spin-oscillator models with three ferromagnetic order parameters and proves the uniqueness of their Gibbsian ground state.

Findings

Models exhibit three ferromagnetic order parameters.

Ground states show maximal ordering.

Unique Gibbsian ground state proven for the simplest model.

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.