Exact Solution of 1D Ising Model on Linear Chain with Arbitrary Spin

2016 ◽  
Vol 845 ◽  
pp. 93-96 ◽  
Author(s):  
Alexey I. Proshkin ◽  
Felix Kassan-Ogly
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Ising Model ◽  
Exact Solutions ◽  
Applied Magnetic Field ◽  
Linear Chain ◽  
Nearest Neighbors ◽  
Arbitrary Spin

We investigated the Ising model on a linear chain with arbitrary spin including interactions between nearest and next-nearest neighbors in an applied magnetic field. A series of exact solutions and formulas for frustration fields, magnetizations and entropies at these fields at T→0 are found.

scholarly journals Critical phenomena in 1D Ising model with arbitrary spin

2018 ◽  
Vol 185 ◽  
pp. 03004 ◽  
Author(s):  
Alexey Proshkin ◽  
Felix Kassan-Ogly ◽  
Alexander Zarubin ◽  
Tatyana Ponomareva ◽  
Ivan Menshikh
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Critical Phenomena ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Spin Correlation ◽  
Arbitrary Spin ◽  
Zero Temperature ◽  
Spin Correlation Function ◽  
Analytical Formulas

The aim of this work was to study critical phenomena taking place in 1D Ising model with different exchange interactions signs and arbitrary spin values in a magnetic field. Exact analytical formulas for frustration fields, zero temperature magnetization and entropy at these fields are obtained. The general behavior of pair spin correlation function with the accounting of only interactions between nearest neighbors is examined.

THE GROUND-STATE PHASE DIAGRAMS OF THE SPIN-2 ISING MODEL

2007 ◽  
Vol 21 (31) ◽  
pp. 5265-5274 ◽  
Author(s):  
AHMET ERDİNÇ
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Ground State ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Biquadratic Exchange ◽  
Model Hamiltonian

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

Exact solution of a two-dimensional Ising model in a random magnetic field

1985 ◽  
Vol 31 (9) ◽  
pp. 6089-6091 ◽  
Author(s):  
G. Forgács ◽  
W. F. Wolff ◽  
A. Süt
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Ising Model ◽  
Two Dimensional ◽  
Random Magnetic Field

Exact solution of the Ising model on checkerboard fractals in an external magnetic field

1998 ◽  
Vol 58 (1) ◽  
pp. 80-85 ◽  
Author(s):  
Tatijana Stošić ◽  
Borko D. Stošić ◽  
F. G. Brady Moreira
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Ising Model ◽  
External Magnetic Field

Some electrically driven flows in magnetohydrodynamics. Part 1. Theory

1968 ◽  
Vol 31 (4) ◽  
pp. 705-722 ◽  
Author(s):  
J. C. R. Hunt ◽  
W. E. Williams
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Approximate Method ◽  
Applied Magnetic Field ◽  
Asymptotic Form ◽  
Magnetohydrodynamic Flow ◽  
Similar Investigation

The magnetohydrodynamic flow between two parallel conducting planes is investigated for the case when the flow is driven by the current produced by electrodes placed one in each plane, the applied magnetic field being perpendicular to the planes. An exact solution is presented for the case of line electrodes placed opposite each other and an approximate method of determining the flow in this case for large Hartman number (M) is also given. It is shown that for large M the asymptotic form of the exact solution agrees with that obtained by the approximate method. The results are generalized to cover the case of line electrodes displaced relative to each other. A similar investigation is carried out for the case of two point electrodes opposite each other.

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