37 research outputs found
Abelian Sandpile Model on the Husimi Lattice of Square Plaquettes
An Abelian sandpile model is considered on the Husimi lattice of square
plaquettes. Exact expressions for the distribution of height probabilities in
the Self-Organized Critical state are derived. The two-point correlation
function for the sites deep inside the Husimi lattice is calculated exactly.Comment: 12 pages, LaTeX, source files and some additional information
available at http://thsun1.jinr.dubna.su/~shcher
Singularites at a Dense Set of Temperature in Husimi Tree
We investigate complex temperature singularities of the three-site
interacting Ising model on the Husimi tree in the presentce of magnetic field.
We show that at certain magnetic field these singularities lie at a dense set
and as a consequence the phase transition condensation take place.Comment: ps file, 10 page
Global Bethe lattice consideration of the spin-1 Ising model
The spin-1 Ising model with bilinear and biquadratic exchange interactions
and single-ion crystal field is solved on the Bethe lattice using exact
recursion equations. The general procedure of critical properties investigation
is discussed and full set of phase diagrams are constructed for both positive
and negative biquadratic couplings. In latter case we observe all remarkable
features of the model, uncluding doubly-reentrant behavior and ferrimagnetic
phase. A comparison with the results of other approximation schemes is done.Comment: Latex, 11 pages, 13 ps figures available upon reques
Quantization of Lie-Poisson structures by peripheric chains
The quantization properties of composite peripheric twists are studied.
Peripheric chains of extended twists are constructed for U(sl(N)) in order to
obtain composite twists with sufficiently large carrier subalgebras. It is
proved that the peripheric chains can be enlarged with additional Reshetikhin
and Jordanian factors. This provides the possibility to construct new solutions
to Drinfeld equations and, thus, to quantize new sets of Lie-Poisson
structures. When the Jordanian additional factors are used the carrier algebras
of the enlarged peripheric chains are transformed into algebras of motion of
the form G_{JB}^{P}={G}_{H}\vdash {G}_{P}. The factor algebra G_{H} is a direct
sum of Borel and contracted Borel subalgebras of lower dimensions. The
corresponding omega--form is a coboundary. The enlarged peripheric chains
F_{JB}^{P} represent the twists that contain operators external with respect to
the Lie-Poisson structure. The properties of new twists are illustrated by
quantizing r-matrices for the algebras U(sl(3)), U(sl(4)) and U(sl(7)).Comment: 24 pages, LaTe
Magnetic and quantum entanglement properties of the distorted diamond chain model for azurite
We present the results of magnetic properties and entanglement of the
distorted diamond chain model for azurite using pure quantum exchange
interactions. The magnetic properties and concurrence as a measure of pairwise
thermal entanglement have been studied by means of variational mean-field like
treatment based on Gibbs-Bogoliubov inequality. Such a system can be considered
as an approximation of the natural material azurite, Cu3(CO3)2(OH)2. For values
of exchange parameters, which are taken from experimental results, we study the
thermodynamic properties, such as azurite specific heat and magnetic
susceptibility. We also have studied the thermal entanglement properties and
magnetization plateau of the distorted diamond chain model for azurite
Magnetic properties and concurrence for fluid 3He on kagome lattice
We present the results of magnetic properties and entanglement for kagome
lattice using Heisenberg model with two-, and three-site exchange interactions
in strong magnetic field. Kagome lattice correspond to the third layer of fluid
3He absorbed on the surface of graphite. The magnetic properties and
concurrence as a measure of pairwise thermal entanglement are studied by means
of variational mean-field like treatment based on Gibbs-Bogoliubov inequality.
The system exhibits different magnetic behaviors, depending on the values of
the exchange parameters (J2, J3). We have obtained the magnetization plateaus
at low temperatures. The central theme of the paper is the comparing the
entanglement and magnetic behavior for kagome lattice. We have found that in
the antiferromagnetic region behaviour of the concurrence coincides with the
magnetization one.Comment: Physics of Atomic Nuclei (accepted for publication) 201
Phase transitions and entanglement properties in spin-1 Heisenberg clusters with single-ion anisotropy
The incipient quantum phase transitions of relevance to nonzero fluctuations
and entanglement in Heisenberg clusters are studied in this paper by exploiting
negativity as a measure in bipartite and frustrated spin-1 anisotropic
Heisenberg clusters with bilinear-biquadratic exchange, single-ion anisotropy
and magnetic field. Using the exact diagonalization technique, it is shown that
quantum critical points signaled by qualitative changes in behavior of
magnetization and particle number are ultimately related to microscopic
entanglement and collective excitations. The plateaus and peaks in spin and
particle susceptibilities define the conditions for a high/low-density quantum
entanglement and various ordered phases with different spin (particle)
concentrations
Yang-Lee Zeros of the Q-state Potts Model on Recursive Lattices
The Yang-Lee zeros of the Q-state Potts model on recursive lattices are
studied for non-integer values of Q. Considering 1D lattice as a Bethe lattice
with coordination number equal to two, the location of Yang-Lee zeros of 1D
ferromagnetic and antiferromagnetic Potts models is completely analyzed in
terms of neutral periodical points. Three different regimes for Yang-Lee zeros
are found for Q>1 and 0<Q<1. An exact analytical formula for the equation of
phase transition points is derived for the 1D case. It is shown that Yang-Lee
zeros of the Q-state Potts model on a Bethe lattice are located on arcs of
circles with the radius depending on Q and temperature for Q>1. Complex
magnetic field metastability regions are studied for the Q>1 and 0<Q<1 cases.
The Yang-Lee edge singularity exponents are calculated for both 1D and Bethe
lattice Potts models. The dynamics of metastability regions for different
values of Q is studied numerically.Comment: 15 pages, 6 figures, with correction
Jordanian Quantum Algebra via Contraction Method and Mapping
Using the contraction procedure introduced by us in Ref. \cite{ACC2}, we
construct, in the first part of the present letter, the Jordanian quantum Hopf
algebra which has a remarkably simple coalgebraic
structure and contains the Jordanian Hopf algebra ,
obtained by Ohn, as a subalgebra. A nonlinear map between and the classical algebra is then established. In the second
part, we give the higher dimensional Jordanian algebras for all . The Universal -matrix of is also given.Comment: 17 pages, Late