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N. S. Ananikian

Publications and source records attributed to N. S. Ananikian.

33 records · Page 2Linked to original sources
arXiv2001

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.

cond-mat.stat-mech↗
arXiv1999

Exact solution of a Z(4) gauge Potts model on planar lattices

The exact solution of a general Z(4) gauge Potts model with a single and double plaquette representation of the action is found on a subspace of gauge-coupling parameters on the square and triangular lattices. The two Ising-type critical lines of a second-order phase transition for the model on a square lattice are found. For the model on a triangular lattice the two critical surfaces of an Ising-type and two nontrivial lines of a second-order phase transition with different critical behavior than on the critical surfaces are found. It is shown that a two dimensional (2D) general Z(4) gauge Potts model with single and double plaquette representation of the action and a 2D spin-3/2 Ising model belong to the same universality class.

cond-mat.stat-mech↗
arXiv1999

Thermodynamic chaos and infinitely many critical exponents in the Baxter-Wu model

The mechanisms leading to thermodynamic chaos in the Baxter-Wu model is considered. We compare the Baxter-Wu model with triangular antiferromagnets and discuss the difficulties related to the modeling of thermodynamic chaos by disordered models. We also discuss how to overcome the problem of infinitely many order parameters. Then we consider the Baxter-Wu model in a complex magnetic field and show the existence of infinitely many critical exponents in this model.

cond-mat.stat-mech↗
arXiv1998

Correlation Functions of the Ising Model with Multisite Interaction on the Husimi Lattice

We consider a general spin-1/2 Ising model with multisite interaction on the Husimi lattice with the coordination number q and derive an analytical expression of correlation functions for stable fixed points of the corresponding recurrence relation. We show that for q=2 our model transforms to the two-state vertex model on the Bethe lattice with q=3 and for the case q=3, with only nearest neighbour interactions, we transform our model to the corresponding model on the Bethe lattice with q=3, using the Yang-Baxter equations.

cond-mat↗
arXiv1998

The Chaotic Properties of the Q-state Potts Model on the Bethe Lattice:Q<2

The Q- state Potts model on the Bethe lattice is investigated for Q<2. The magnetization of this model exhibits a complicated behavior including both the period doubling bifurcation and chaos. The Lyapunov exponents of the Potts-Bethe map are considered as order parameters. We find a scaling behavior in the distribution of Lyapunov exponents in fully developed chaotic case. Using the thermodynamic formalism of dynamical systems have we investigated the nonanalytic behavior in the distribution of Lyapunov exponents and located the point of phase transition of the ''chaotic free energy''.

cond-mat↗
arXiv1998

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.

cond-mat.stat-mech↗
arXiv1997

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.

hep-lat↗
arXiv1997

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.

cond-mat↗
arXiv1997

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.

cond-mat↗
arXiv1996

Thermodynamc Approach to Three-Site Antiferromagnetic Ising Model in Chaotic Region

The chaotic properties of the three-site antiferromagnetic Ising model on Husimi tree are investigated in magnetic field. Macroscopic quantity of three-site antiferromagnetic Ising model is generated by one dimensional map. It is shown that in certain parameter setting strange attractors of this map exhibit multifractal scaling. By applying thermodynamic formalism we find nonanalyticity in free energy as well as in entropy. We show that the temperature of phase transition depends on parameter of model and varies from negative to positive value.

cond-mat.stat-mech↗
arXiv1995

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.

cond-mat↗
arXiv1995

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" $ β_c = 0.89 $. We obtain the density of the invariant measure on the chaotic repeller.

cond-mat↗
arXiv1994

Tricritical Phenomena in a Z(3) Lattice Gauge Theory

The Z(3) gauge model with double plaquette representation of the action on a generalized Bethe lattice of plaquettes is constructed. It is reduced to the spin-1 Blume-Emery-Griffiths (BEG) model. An Ising-type critical line of a second-order phase transition ending in the tricritical point is found.

hep-lat↗
arXiv1994

The Multisite Antiferromagnetic Ising Spin Model and Universality of Feigenbaum Constants

The Feigenbaum constants $α$ and $δ$ for the three-site antiferromagnetic Ising spin model on Husimi tree are calculated. It is shown that the numerical values of these constants for this real physical system coincide with the famous universal Feigenbaum constants with high accuracy. The quantitative description from ordering to chaos is also obtained.

hep-th↗