Differential Operator Technique in the Ising Spin Systems

Kaneyoshi, T.

doi:10.12693/aphyspola.83.703

Cited by 332 publications

(196 citation statements)

References 37 publications

(72 reference statements)

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“…If these large magnetic fields are dominant against the ferromagnetic exchange interactions such as h = 3.0 >> R, in this case, spin-up and spin-down states are canceled out, and the overall system behaves like spin-0. This concept is very similar to that observed in the spin-1 Ising system, when the crystal field D takes a large negative critical value [36]. Besides, in the presence of a continuous probability distribution such as a Gaussian, the system has been found to exhibit only second order phase transitions [19].…”

supporting

confidence: 57%

Critical behavior and universality properties of uniaxial ferromagnetic thin films in the presence of random magnetic fields

Yüksel

2015

Journal of Magnetism and Magnetic Materials

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Critical phenomena in uniaxial ferromagnetic thin films in the presence of random magnetic fields have been studied within the framework of effective field theory. When the type of the random field distribution is bimodal, the system exhibits tricritical behavior. Furthermore, the critical value of surface to bulk ratio of exchange interactions at which the transition temperature becomes independent of film thickness is insensitive to the presence of disorder whether the distribution is bimodal or trimodal. Regarding the universality properties, neither p, nor h variations in the system can affect the value of the shift exponent λ. In this regard, it can be concluded that pure ferromagnetic thin films are in the same universality class with those under the influence of random discrete magnetic fields.

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supporting

confidence: 57%

Critical behavior and universality properties of uniaxial ferromagnetic thin films in the presence of random magnetic fields

Yüksel

2015

Journal of Magnetism and Magnetic Materials

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“…The function F ({x i }) is nothing but just the replacement of all h i terms by x i , in Eq. (12). We note that, expression given by Eq.…”

Section: N-spin Clustermentioning

confidence: 94%

Effective field theory in larger clusters – Ising model

Akıncı

2015

Journal of Magnetism and Magnetic Materials

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General formulation for the effective field theory with differential operator technique and the decoupling approximation with larger finite clusters (namely EFT-N formulation) has been derived, for S-1/2 bulk systems. The effect of the enlarging this finite cluster on the results in the critical temperatures and thermodynamic properties have been investigated in detail. Beside the improvement on the critical temperatures, the necessity of using larger clusters, especially in nano materials have been discussed. With the derived formulation, application on the effective field and mean field renormalization group techniques also have been performed. IntroductionCooperative phenomena in magnetic systems are often investigated within some approximation methods in statistical physics. There are still a few exact results in the literature [1], since the partition function is not tractable in most of the systems. The most known example of this situation is that there is still no exact result for the most basic model of magnetic systems, namely Ising model [2] in three dimensions, although exact result for two dimensional system has been presented in 1944 [3]. There are numerous approximation and simulation methods for these systems. Each of these methods have their own advantages as well as disadvantages. A class of these approximation methods is called effective field theories (EFT) [4]. Recent developments in these formulations, especially in correlated effective theories can be found in Ref. [5].Early attempts to solve Ising model yields mean field theories (MFT), which reduce the many particle Hamiltonian into one particle, with replacing the spin operators in the Hamiltonian with their thermal (or ensemble) averages. This means that neglecting all self-spin and multi-spin correlations in the system. After than, by handling the self-spin correlations, EFT formulations have been constructed. First successful variants of these approximations are Oguchi approximation [6] and Bethe-Peierls approximation (BPA) [7,8]. After than, many variants of the EFT constructed with their own advantages, disadvantages and own limitations [5].Most of the EFT formulations start by constructing a finite cluster within the system. Interactions between the spins which are located in this cluster are written exactly as much as possible and the coupling of this cluster with the 1 umit.akinci@deu.edu.tr 1

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“…(3) one can use the differential operator technique [23,24]. By using the differential operator technique, Eq.…”

Section: Formulationmentioning

confidence: 99%

“…It is well known that MFA neglects the thermal fluctuations via neglecting the self spin correlations whereas the effective field theory (EFT) which is superior to conventional MFA is based on the differential operator technique [23,24] and it takes into account the self spin correlations. Thus, it is expected from EFT to obtain more reasonable results than MFA for these systems, as in the case of static Ising model.…”

Section: Introductionmentioning

confidence: 99%

Effective field investigation of dynamic phase transitions for site diluted Ising ferromagnets driven by a periodically oscillating magnetic field

Akıncı

Yüksel

Vatansever

et al. 2012

Physica A: Statistical Mechanics and its Applications

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Abstract. Dynamic behavior of a site diluted Ising ferromagnet in the presence of periodically oscillating magnetic field has been analyzed by means of the effective field theory (EFT). Dynamic equation of motion have been solved for a honeycomb lattice (z = 3) with the help of a Glauber type stochastic process. The global phase diagrams and the variation of the corresponding dynamic order parameter as a function of the Hamiltonian parameters and temperature has been investigated in detail and it has been shown that the system exhibits reentrant phenomena, as well as a dynamic tricritical point which disappears for sufficiently weak dilution.

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Differential Operator Technique in the Ising Spin Systems

Abstract: A review is given of the differential operator technique in the Ising spin systems. The theoretical frameworks of the various models are discussed on the basis of the Ising spin identities. These can be applied to examine the magnetic properties in a variety of magnetic materials.

Cited by 332 publications

References 37 publications

Critical behavior and universality properties of uniaxial ferromagnetic thin films in the presence of random magnetic fields

Critical behavior and universality properties of uniaxial ferromagnetic thin films in the presence of random magnetic fields

Effective field theory in larger clusters – Ising model

Effective field investigation of dynamic phase transitions for site diluted Ising ferromagnets driven by a periodically oscillating magnetic field

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