7 research outputs found
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
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
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