Dynamic magnetic properties the spin-1 Ising model with bilinear and biquadratic interactions within the path probability method

2019 ◽  
Vol 526 ◽  
pp. 120933 ◽  
Author(s):  
Mehmet Ertaş ◽  
Mustafa Keskin
Keyword(s):  
Magnetic Properties ◽  
Ising Model ◽  
Probability Method ◽  
Path Probability Method

Relaxation times obtained from the rate equations using path probability method for the spin-1 Ising model

2019 ◽  
Vol 33 (22) ◽  
pp. 1950258 ◽  
Author(s):  
Rıza Erdem ◽  
Songül Özüm
Keyword(s):  
Ising Model ◽  
Relaxation Times ◽  
Phenomenological Theory ◽  
Equilibrium States ◽  
Time Dependent ◽  
Rate Equations ◽  
Probability Method ◽  
Temperature Variations ◽  
Path Probability Method ◽  
Good Agreement

We have presented the time-dependent behaviors of a spin-1 Ising model (with both bilinear and biquadratic interactions) in the neighborhood of the equilibrium states via the path probability method. The rate equations as introduced by Keskin and co-workers (1989) have been linearized to obtain the characteristic relaxation times. The temperature variations of these times were produced in accordance with the Tanaka and Mannari’s work (1976) on the equilibrium properties. Results are compared to one using Onsager’s phenomenological theory and a good agreement is achieved.

Determination of the steady-state kinetics in a spin-1 Ising model using path probability method

2020 ◽  
Vol 34 (30) ◽  
pp. 2050338 ◽  
Author(s):  
Songül Özüm ◽  
Rıza Erdem
Keyword(s):  
Steady State ◽  
Ising Model ◽  
Linear Equations ◽  
Kinetic Equations ◽  
Phenomenological Approach ◽  
Rate Equations ◽  
Probability Method ◽  
Steady State Kinetics ◽  
Path Probability Method

As a continuation of our previously published work, we propose a theoretical framework for the determination of steady-state kinetics in a spin-1 Ising model by the path probability method. The framework is based on the principles of non-equilibrium statistical physics and is quite different from the phenomenological approach. We construct a set of linear kinetic equations for the order parameters using the non-linear dynamic (or rate) equations in the presence of external magnetic field. From the steady-state solutions of the linear equations, an expression for the complex (or dynamic) magnetic susceptibility [Formula: see text] is derived. The temperature dependence of the magnetic dispersion relation [Formula: see text] and magnetic absorption factor [Formula: see text] has been studied in the ferromagnetic (FM) and paramagnetic (PM) phases as well as near the critical regime.

Spin Kinetics Studied by Path Probability Method

1993 ◽  
Vol 95-98 ◽  
pp. 119-124 ◽  
Author(s):  
Tetsuo Mohri ◽  
Takayasu Ikegami
Keyword(s):  
Probability Method ◽  
Path Probability Method
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