The bilayer Ising model and a generalized Husimi tree approximation

James L Monroe

doi:10.1016/j.physa.2003.12.018

The bilayer Ising model and a generalized Husimi tree approximation

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2003.12.018 ◽

2004 ◽

Vol 335 (3-4) ◽

pp. 563-576 ◽

Cited By ~ 22

Author(s):

James L Monroe

Keyword(s):

Ising Model ◽

Tree Approximation ◽

Husimi Tree

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Surface magnetic order in the Ising model: A Cayley tree approximation

Physics Letters A ◽

10.1016/0375-9601(77)90959-8 ◽

1977 ◽

Vol 62 (2) ◽

pp. 93-94 ◽

Cited By ~ 3

Author(s):

Félix Yndurain

Keyword(s):

Ising Model ◽

Cayley Tree ◽

Magnetic Order ◽

Tree Approximation

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Strange Attractors in an Antiferromagnetic Ising Model

Fractals ◽

10.1142/s0218348x97000176 ◽

1997 ◽

Vol 05 (01) ◽

pp. 175-185 ◽

Cited By ~ 18

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.

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