7 research outputs found
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
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.Comment: 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 change
Long Cycles in a Perturbed Mean Field Model of a Boson Gas
In this paper we give a precise mathematical formulation of the relation
between Bose condensation and long cycles and prove its validity for the
perturbed mean field model of a Bose gas. We decompose the total density
into the number density of
particles belonging to cycles of finite length () and to
infinitely long cycles () in the thermodynamic limit. For
this model we prove that when there is Bose condensation,
is different from zero and identical to the condensate density. This is
achieved through an application of the theory of large deviations. We discuss
the possible equivalence of with off-diagonal long
range order and winding paths that occur in the path integral representation of
the Bose gas.Comment: 10 page