100 research outputs found
Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
We consider the superstable cycles of the Q-state Potts (QSP) and the
three-site interaction antiferromagnetic Ising (TSAI) models on recursive
lattices. The rational mappings describing the models' statistical properties
are obtained via the recurrence relation technique. We provide analytical
solutions for the superstable cycles of the second order for both models. A
particular attention is devoted to the period three window. Here we present an
exact result for the third order superstable orbit for the QSP and a numerical
solution for the TSAI model. Additionally, we point out a non-trivial
connection between bifurcations and superstability: in some regions of
parameters a superstable cycle is not followed by a doubling bifurcation.
Furthermore, we use symbolic dynamics to understand the changes taking place at
points of superstability and to distinguish areas between two consecutive
superstable orbits.Comment: 12 pages, 5 figures. Updated version for publicatio
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
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