Bethe lattice consideration of the antiferromagnetic spin-1 Ising model

The outcome of the random crystal field effects on the antiferromagnetic spin-1 Blume–Capel model and external magnetic field are examined on the Bethe Lattice in terms of exact recursion relations. It is assumed that the crystal field is either turned on or off randomly with probability [Formula: see text] and [Formula: see text], respectively. The phase diagrams are constructed from the thermal analysis of the order parameters with the coordination number [Formula: see text] which corresponds to honeycomb lattice. It is explored that the system goes both second- and first-order phase transitions, along with the reentrant behavior and a few critical points. The reentrant behavior is stronger for lower values of [Formula: see text] and disappears as [Formula: see text] gets closer to 1.0. The first-order lines are observed to be either linked to the tricritical points or decomposed. The critical end points and double critical points are also observed.

Download Full-text

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

International Journal of Modern Physics C ◽

10.1142/s0129183103005443 ◽

2003 ◽

Vol 14 (10) ◽

pp. 1305-1320 ◽

Cited By ~ 14

Author(s):

BÜLENT KUTLU

Keyword(s):

Phase Transition ◽

Ising Model ◽

Cellular Automaton ◽

Intermediate Phase ◽

Finite Size ◽

Square Lattice ◽

Two Dimensional ◽

Finite Size Scaling ◽

Creutz Cellular Automaton ◽

Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

Download Full-text

Triple mixed-spin Ising model

International Journal of Modern Physics B ◽

10.1142/s0217979220501295 ◽

2020 ◽

Vol 34 (13) ◽

pp. 2050129

Author(s):

Erhan Albayrak

Keyword(s):

Phase Transitions ◽

Ising Model ◽

Magnetic Fields ◽

Exchange Interaction ◽

Spin System ◽

Bethe Lattice ◽

Nearest Neighbors ◽

Recursion Relations ◽

Mixed Spin ◽

Exchange Interaction Parameter

The A, B and C atoms with spin-1/2, spin-3/2 and spin-5/2 are joined together sequentially on the Bethe lattice in the form of ABCABC[Formula: see text] to simulate a molecule as a triple mixed-spin system. The spins are assumed to be interacting with only their nearest-neighbors via bilinear exchange interaction parameter in addition to crystal and external magnetic fields. The order-parameters are obtained in terms of exact recursion relations, then from the study of their thermal variations, the phase diagrams are calculated on the possible planes of our system. It is found that the model gives only second-order phase transitions in addition to the compensation temperatures.

Download Full-text