79 research outputs found
Arnold Tongues and Feigenbaum Exponents of the Rational Mapping for Q-state Potts Model on Recursive Lattice: Q<2
We considered Q-state Potts model on Bethe lattice in presence of external
magnetic field for Q<2 by means of recursion relation technique. This allows to
study the phase transition mechanism in terms of the obtained one dimensional
rational mapping. The convergence of Feigenabaum and
exponents for the aforementioned mapping is investigated for the period
doubling and three cyclic window. We regarded the Lyapunov exponent as an order
parameter for the characterization of the model and discussed its dependence on
temperature and magnetic field. Arnold tongues analogs with winding numbers
w=1/2, w=2/4 and w=1/3 (in the three cyclic window) are constructed for Q<2.
The critical temperatures of the model are discussed and their dependence on Q
is investigated. We also proposed an approximate method for constructing Arnold
tongues via Feigenbaum exponent.Comment: 15 pages, 12 figure
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
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