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Dynamic susceptibility for a spin-1 Isingmodel using the path probability method

Songül Özüm, Rıza Erdem

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

The nonlinear rate equations based on the path probability method is used to derive the dynamic (or complex) susceptibility ( ? ) for a spin-1 Ising model with bilinear and biquadratic interactions when the external magnetic field exists. Firstly, the rate equations are linearized. Then, these are solved in the presence of an oscillating external magnetic field. From the real and imaginary parts of ? , the magnetic dispersion and absorption factors are found. Temperature dependence of these quantities in the ferromagnetic and paramagnetic phase regions (as well as their critical properties) are presented. Finally, the theoretical results are compared with those obtained using irreversible thermodynamics

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Chinese Physics B•Aug 1, 2010•9 citations
The nonlinear rate equations based on the path probability method is used to derive the dynamic (or complex) susceptibility ( ? ) for a spin-1 Ising model with bilinear and biquadratic interactions when the external magnetic field exists. Firstly, the rate equations are linearized. Then, these are solved in the presence of an oscillating external magnetic field. From the real and imaginary parts of ? , the magnetic dispersion and absorption factors are found. Temperature dependence of these quantities in the ferromagnetic and paramagnetic phase regions (as well as their critical properties) are presented. Finally, the theoretical results are compared with those obtained using irreversible thermodynamics
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.
Abstract Utilizing the path probability method, we investigated nonequilibrium magnetic features in a mixed spin (2, 5/2) Ising model Hamiltonian composed of bilinear and crystal-field interactions in the presence of an external oscillating magnetic field. We numerically solved the time dependence of average magnetizations to find the phases in the system. We examined the dynamic magnetizations to obtain dynamic phase transition (DPT) temperatures, the nature of the DPTs, and phases in the system. The dynamic phase diagrams (DPDs) were constructed in reduced temperature and the amplitude of oscillating magnetic field plane for various interaction parameters. We observed that the system gives very rich and interesting topological behaviors of DPDs, such as up to two dynamic tricritical points, six critical end points, a double critical end points, a zero-temperature critical point, one inverse critical end point and a quadruple point depending on interaction parameters. The system also exhibits paramagnetic, six distinct ferrimagnetic and three different nonmagnetic phases as well as up to eleven different mixed or hybrid phases. In addition, the system exhibits the reentrant behavior.
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.
Kinetics of the mixed spin (1, 3/2) Ising ferrimagnetic system on the two interpenetrating square lattices with the bilinear and crystal-field interactions under an oscillating magnetic field were investigated by using the path probability method (PPM). We examined time variations in average dynamic magnetizations and obtained phases and then we investigated the thermal behaviors of dynamic magnetizations to determine the nature of the dynamic phase transitions and find their temperature values. We also constructed the dynamic phase diagrams in (d,T) and (h_0,T) planes. Dynamic phase diagrams display the paramagnetic (p), ferrimagnetic (i), and mixed phases (i+p), and one dynamic tricritical point and dynamic double critical endpoints. We found that the PPM is a more convenient method to investigate the kinetics and dynamics behaviors of ferrimagnetism.
Dynamic behavior of a spin-1 Ising model [1] with arbitrary bilinear (J) and biquadratic (K) pair interactions is studied by using the path probability method [2]. First the equilibrium behavior of the model is given briefly in order to understand the nonequilibrium behavior. Then the path probability method is applied to the spin-1 Ising model with J and K Hamiltonian and the system of nonlinear differential equations, which are also called the dynamic equations or rate equations, is found. The dynamic equations are solved using the Runga-Kutta method and the solutions, namely relaxation of order parameters are examined to see the "flatness" property of metastable states. It is found that the system relaxes to either stable or metastable states depending upon the initial values of the order parameters. Moreover, if there are more than one metastable states, the relaxation occurs according to the initial values of the order parameters or free energy values. Finally, the results are compared with the flow diagrams which are the solutions of the dynamic equations in two-dimensional phase space [3] and it is seen that the same results are found except for the "flatness" property of metastable states.
Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics. First, the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures, i.e. the first- and second-order and the tricritical points. Then, the Onsager theory is applied to the model and the kinetic or rate equations are obtained. By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points. Moreover, the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically, and they are found to be in good agrement.