Strange Attractors in an Antiferromagnetic Ising Model

Fractals ◽  
1997 ◽  
Vol 05 (01) ◽  
pp. 175-185 ◽  
Author(s):  
N. S. Ananikian ◽  
S. K. Dallakian ◽  
N. Sh. Izmailian ◽  
K. A. Oganessyan
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Thermodynamic Formalism ◽  
Positive Temperature ◽  
Chaotic Region ◽  
Negative Temperatures ◽  
Fully Developed Chaos ◽  
Statistical Mechanical ◽  
Husimi Tree ◽  
Antiferromagnetic Ising Model

The three-site antiferromagnetic Ising model on Husimi tree is investigated in an external magnetic field. The full bifurcation diagram, including chaos, of the magnetization is exhibited. With the "thermodynamic formalism", we investigate the antiferromagnetic Ising model in the case of fully developed chaos and describe the chaotic properties of this statistical mechanical system via the invariants characterizing a strange attractor. It is shown that this system displays in the chaotic region a phase transition at a positive "temperature" whereas in a class of maps close to x→ 4x(1-x), the phase transitions occur at negative "temperatures". The Frobenius-Perron recursion equation is numerically solved and the density of the invariant measure is obtained.

Adiabatic demagnetization at absolute negative temperature: Generation of quantum correlations

2019 ◽  
Vol 17 (03) ◽  
pp. 1950023
Author(s):  
Gregory B. Furman ◽  
Shaul D. Goren ◽  
Victor M. Meerovich ◽  
Vladimir L. Sokolovsky
Keyword(s):  
Magnetic Field ◽  
Negative Temperature ◽  
Quantum Correlations ◽  
Zero Magnetic Field ◽  
Positive Temperature ◽  
Nuclear Spins ◽  
Adiabatic Demagnetization ◽  
Negative Temperatures ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

In this paper, we study behavior of the correlations, both quantum and classical, under adiabatic demagnetization process in systems of nuclear spins with dipole–dipole interactions in an external magnetic field and in the temperature range including positive and negative temperatures. For a two-spin system, analytical expressions for the quantum and classical correlations are obtained. It is revealed that the field dependences of the quantum and classical correlations at positive and negative temperatures are substantially different. This difference most clearly appears in the case of zero magnetic field: at negative temperature, the measures of quantum correlations tend to the maximum values with a temperature increase. At positive temperature, these quantities tend to zero at a decrease of magnetic field. It is also found that, for the nearest-neighboring spins in the same field, the values of concurrence and discord are larger at negative temperatures than at positive ones.

PHASE BOUNDARY AND UNIVERSALITY OF THE TRIANGULAR LATTICE ANTIFERROMAGNETIC ISING MODEL

1992 ◽  
Vol 06 (17) ◽  
pp. 2913-2924 ◽  
Author(s):  
JAE DONG NOH ◽  
DOOCHUL KIM
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Phase Boundary ◽  
Triangular Lattice ◽  
Central Charge ◽  
Universality Class ◽  
Zero Field ◽  
Crossover Effect ◽  
Matrix Methods ◽  
Antiferromagnetic Ising Model

Transfer matrix methods are used to locate accurate phase boundary of the triangular lattice antiferromagnetic Ising model in magnetic field. Universal quantities such as the central charge and the first few scaling dimensions are obtained along the phase boundary except near the zero field point where the crossover effect degrades convergence. Numerical results are fully consistent with the operator content of the 3-state Potts model indicating that whole phase boundary belongs to the 3-state Potts universality class.

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