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Chinese Physics B

Relaxation theory of spin-3/2 Ising system near phase transition temperatures

Osman Canko, Mustafa Keskín

Published Aug 1, 2010• 9 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/19/8/080516

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Analytical expressions of the order parameters near the transition temperatures in the spin-3/2 Ising system with bilinear (J) and biquadratic (K) interactions are presented for various values of J/K. First, we obtain the free energy expression and the equations to determine order parameters by using the mean-field approximation. Then, the order parameters are expressed in the vicinity of the transition temperatures in which these expressions are very important to study the dynamics of the system by means of Onsager's theory of irreversible thermodynamics. Hence, we investigate the phase transitions occurring in the system and also obtain two tricritical points analytically. Finally, the specific heat and magnetic susceptibility are calculated and an argument about the critical exponents at the second-order phase transitions and tricritical points is given.

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Journal of Physics Condensed Matter•Jan 6, 1992•10 citations
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.
Analytical expressions of the order parameters near the transition temperatures in the spin-3/2 Ising system with bilinear (J) and biquadratic (K) interactions are presented for various values of J/K. First, we obtain the free energy expression and the equations to determine order parameters by using the mean-field approximation. Then, the order parameters are expressed in the vicinity of the transition temperatures in which these expressions are very important to study the dynamics of the system by means of Onsager's theory of irreversible thermodynamics. Hence, we investigate the phase transitions occurring in the system and also obtain two tricritical points analytically. Finally, the specific heat and magnetic susceptibility are calculated and an argument about the critical exponents at the second-order phase transitions and tricritical points is given.
The dynamical phase transitions of the kinetic Ising model in the presence of a random magnetic field with a bimodal probability distribution is studied by using effective-field theory (EFT) with correlations. We have used a Glauber-type stochastic dynamic to describe the time evolution of the system, where the system strongly depends on the H≡√<H(i)(2)>(c) root mean square deviation of the magnetic field. The EFT dynamic equation is given for the simple cubic lattice (z=6), and the dynamic order parameter is calculated. The system presents ferromagnetic and paramagnetic states for low and high temperatures, respectively. Our results predict first-order transitions at low temperatures and large disorder strengths, which corresponds to the existence of a nonequilibrium tricritical point (TCP) in a phase diagram in the T-H plane. We compare the results with the equilibrium phase diagram, where only the first-order line is different. Our qualitative results are compatible with recent Monte Carlo simulations.
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.
Critical behaviors of the sound attenuation in a spin-1 Ising system with bilinear (J) and biquadratic (K) interactions are investigated within the framework of cluster variation method and Onsager theory of irreversible thermodynamics. The sound wave is assumed to couple mainly to the order parameter fluctuations which decay via order parameter relaxation processes. Two relaxation times are obtained and an expression is found for the sound attenuation coefficient (α) in terms of these relaxation times. The temperature behavior of the sound attenuation near the phase transition temperatures (Tc) is analyzed according to various values of Onsager coefficients (γij) and sound frequency (ω). For T<Tc it is found that the maxima of the attenuation shifted to lower temperatures with increasing ω and γij (i≠j) values. For T>Tc the data give evidence that there is no relaxational contribution to sound attenuation coming from order parameter fluctuations. On the other hand, a convergence is found in attenuation just below the critical and the tricritical points as (Tc−T), while a jump-discontinuity is observed for the first-order behavior. The frequency variation of the sound attenuation is also investigated and in addition to ω2-attenuation dependence observed in the hydrodynamic regime it is observed that in the high frequency region the attenuation is independent of ω and the ratio of two interaction parameters (J/K).
The two-state Ising model with nearest-neighbour bilinear exchange constant J (2) , three-spin coupling constant J (3) and four-spin coupling constant J (4) is studied using the effective-field approximation. The temperature variation in spontaneous magnetization is studied for different coordination numbers z and for various values of the parameters alpha =J (3) /J (2) and alpha '=J (4) /J (2) . It is seen that, in the absence of three-spin coupling, there exists a critical value of alpha ' (say, alpha ' c ) above which the magnetization becomes double valued at and beyond the Curie temperature T c , forming a bulge near T c which indicates the occurrence of a first-order transition. The expressions for alpha ' c for z=3, 4, 6 are derived and it is found that alpha ' c increases as z increases. In the absence of four-spin coupling it is found that first-order transitions appear for alpha >or=0. The magnetization curves are also studied for the case when all the interactions are present. The results are discussed with reference to those obtained from the molecular-field approximation.