24 research outputs found
An Ising spin - S model on generalized recursive lattice
The Ising spin - S model on recursive p - polygonal structures in the
external magnetic field is considered and the general form of the free energy
and magnetization for arbitrary spin is derived. The exact relation between the
free energies on infinite entire tree and on its infinite "interior" is
obtained.Comment: 9 pages, 1 figure, to be published in Physica
Chaos in the Z(2) Gauge Model on a Generalized Bethe Lattice of Plaquettes
We investigate the Z(2) gauge model on a generalized Bethe lattice with three
plaquette representation of the action. We obtain the cascade of phase
transitions according to Feigenbaum scheme leading to chaotic states for some
values of parameters of the model. The duality between this gauge model and
three site Ising spin model on Husimi tree is shown. The Lyapunov exponent as a
new order parameter for the characterization of the model in the chaotic region
is considered. The line of the second order phase transition, which corresponds
to the points of the first period doubling bifurcation, is also obtained.Comment: LaTeX, 7 pages, 4 Postscript figure
The Phase Structure of Antiferromagnetic Ising Model in the Presence of Frustrations
The antiferromagnetic Ising model in a magnetic field is considered on the
Husimi tree. Using iteration technique we draw the plots of magnetization
versus external field for different temperatures and construct the resulting
phase diagram. We show that frustration effects essentially change the critical
properties. The model exhibits three distinct critical regions, including
re-entrant phase structure and Griffiths singularities.Comment: 5 pages, 5 figures, submited to Phys. Lett.
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
Chaotic Repellers in Antiferromagnetic Ising Model
For the first time we present the consideration of the antiferromagnetic
Ising model in case of fully developed chaos and obtain the exact connection
between this model and chaotic repellers. We describe the chaotic properties of
this statistical mechanical system via the invariants characterizing a fractal
set and show that in chaotic region it displays phase transition at {\it
positive} "temperature" . We obtain the density of the
invariant measure on the chaotic repeller.Comment: LaTeX file, 10 pages, 4 PS figurs upon reques
Yang-Lee and Fisher Zeros of Multisite Interaction Ising Models on the Cayley-type Lattices
A general analytical formula for recurrence relations of multisite
interaction Ising models in an external magnetic field on the Cayley-type
lattices is derived. Using the theory of complex analytical dynamics on the
Riemann sphere, a numerical algorithm to obtain Yang-Lee and Fisher zeros of
the models is developed. It is shown that the sets of Yang-Lee and Fisher zeros
are almost always fractals, that could be associated with Mandelbrot-like sets
on the complex magnetic field and temperature planes respectively.Comment: 9 pages, 3 figures; with minor correction
An exact solution on the ferromagnetic Face-Cubic spin model on a Bethe lattice
The lattice spin model with --component discrete spin variables restricted
to have orientations orthogonal to the faces of -dimensional hypercube is
considered on the Bethe lattice, the recursive graph which contains no cycles.
The partition function of the model with dipole--dipole and
quadrupole--quadrupole interaction for arbitrary planar graph is presented in
terms of double graph expansions. The latter is calculated exactly in case of
trees. The system of two recurrent relations which allows to calculate all
thermodynamic characteristics of the model is obtained. The correspondence
between thermodynamic phases and different types of fixed points of the RR is
established. Using the technique of simple iterations the plots of the zero
field magnetization and quadrupolar moment are obtained. Analyzing the regions
of stability of different types of fixed points of the system of recurrent
relations the phase diagrams of the model are plotted. For the phase
diagram of the model is found to have three tricritical points, whereas for there are one triple and one tricritical points.Comment: 20 pages, 7 figure
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