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The Turkish economy between 2002-2019 period has been investigated within the econophysical approach. From the individual income data obtained from the Household Budget Survey, the Gompertz-Pareto distribution for each year and Goodwin cycle for the mentioned period have been obtained. For this period, in which thirteen elections were held under the single-party rule, it has been observed that the income distribution fits well with the Gompertz-Pareto distribution which shows the two-class structure of the Turkish economy. The variation of the threshold value $x_t$ (which separates these two classes) as well as Pareto coefficient have been obtained. Besides, Goodwin cycle has been observed within this period, centered at $(u,v)\cong (66.30,83.40)$ and a period of $T=18.30$ years. It has been concluded that these observations are consistent with the economic and social events experienced in the mentioned period.

The isothermal magnetic entropy change has been obtained for the bilayer system that consists of $S_u$ and $S_l$ valued spins in each layer. The relation between the IMEC and the spin value as well as the value of exchange interaction between two layers have been obtained. Recently experimentally given double peaks behavior for manganite bilayers has been demonstrated theoretically, and explanation is given. On the other hand, the conditions that give rise to transition from this double peak behavior to the single peak behavior have been obtained and discussed.

The magneticaloric properties of the Ising nanotube constituted by arbitrary core spin values $S_c$ and the shell spin values $S_s$ have been investigated by mean field approximation. During this investigation, several quantities have been calculated, such as isothermal magnetic entropy change, full width at half maximum value and the refrigerant capacity. The variation of these quantities with the values of the spins and exchange interaction between the core and shell is determined. Besides, recently experimentally observed double peak behavior in the variation of the isothermal magnetic entropy change with the temperature is obtained for the nanotube.

In this study, hysteresis characteristics of the generalized spin-S binary alloy represented by the formula $A_c B_{1-c}$ have been investigated within the framework of effective field approximation. The binary system consists of type A (spin-S) and type B (spin-S) atoms which are randomly distributed on a honeycomb lattice. Both integer and half-integer spin models of two magnetic atom types are examined. By detailed investigation on hysteresis loops, multiple hysteresis behaviors are obtained for a given set of Hamiltonian parameters. Besides, the quantities of hysteresis characteristics as the hysteresis loop area, remanent magnetization, and coercive field have been investigated as functions of concentration.

Critical properties of the generalized spin-S magnetic binary alloys represented by $A_{c}B_{1-c}$ have been investigated within the framework of EFT. By inspecting the evolution of the phase diagrams with the concentration for several spin values, general results have been obtained. Obtained results cover the results obtained for special cases in the literature. Type of the transition (first/second order), as well as the presence of the tricritical point have been determined for general spin models. It has also been shown that, the same critical concentration value exist in the system, regardless of the spin value for binary alloy consist of half integer-integer spin alloy.

The magnetocaloric properties of the Ising binary alloys composed of arbitrary spin values, have been determined by using effective field theory. For determining the efficiency of the magnetocaloric effect in binary alloy, the quantities of interest such as isothermal magnetic entropy change and refrigerant capacity have been calculated for various values of spin and concentration. It is shown that, by changing the concentration we can tune the magnetocaloric performance. Also, it has been shown that greater refrigerant capacity can be obtained for intermediate concentration values, in comparison with the limiting concentration values.

Magnetic properties of the multi-walled nanotubes have been investigated. Heisenberg model, which is a suitable model for the system consist of atoms with localized wave functions has been used. Effective field theory in two spin cluster for spin-1/2 has been numerically solved and critical properties such as phase diagrams as well as the behavior of the order parameter and hysteresis loops obtained.

The dynamical Ising model under the effect of the amplitude modulated time dependent periodic magnetic field has been solved by using EFT with Glauber type of stochastic process. Several cases with amplitude modulation have been investigated. It has been shown that, amplitude modulation could display dynamical phase transition on the magnetic system.

Hysteresis behaviors of the binary alloy system represented by the formula $A_c B_{1-c}$ have been investigated within the framework of EFT. The system consists of type A atoms (spin-$1$) with concentration $c$ and type B atoms (spin-$1/2$) with concentration $1-c$. After giving the phase diagrams, we focused on the different type of hysteresis behaviors in the system. Especially, the mechanisms giving rise to double hysteresis behavior have been explained, which appear at large negative values of the crystal field and low temperatures. It has been observed that binary alloy system could exhibit DH behavior in region $0

Hysteresis characteristics of the crystal field diluted general Spin-S ($S>1$) Blume-Capel model have been studied within the effective field approximation. Particular emphasis has been paid on the large negative valued crystal field and low temperature region and it has been demonstrated for this region that, rising dilution of the crystal field results in decreasing number of windowed hysteresis loops. The evolution of the multiple hysteresis loop with the dilution of the crystal field has been investigated and physical mechanism behind this evolution has been given.

Hysteresis characteristics of the general Spin-S ($S>1$) Blume-Capel model have been studied within the effective field approximation. Particular emphasis has been paid on the large negative valued crystal field region and it has been demonstrated for this region that, Spin-S Blume-Capel model has $2S$ windowed hysteresis loop in low temperatures. Some interesting results have been obtained such as nested characteristics of the hysteresis loops of successive spin-S Blume-Capel model. Effect of the rising crystal field and temperature on these hysteresis behaviors have been investigated in detail and physical mechanisms have been given.

Dynamic behaviour of an isotropic Ashkin-Teller model in the presence of a periodically oscillating magnetic field has been analysed by means of the mean field approximation. The dynamic equation of motion has been constructed with the help of a Glauber type stochastic process and solved for a square lattice. After defining the possible dynamical phases of the system, phase diagrams have been given and the behaviour of the hysteresis loops has been investigated in detail. The hysteresis loop for specific order parameter of isotropic Ashkin-Teller model has been defined and characteristics of this loop in different dynamical phases have been given., Comment: 13 pages, 7 figures

The effect of the anisotropy in the exchange interaction and film thickness on the hysteresis behavior of the anisotropic Heisenberg thin film has been investigated with effective field formulation in a two spin cluster using the decoupling approximation. The behaviors of the hysteresis loop area, coersive field and remanent magnetization with the film thickness and anisotropy in the exchange interaction have been obtained.

The hysteresis behaviors of anisotropic S-1 Heisenberg model have been studied within the effective field theory with two spin cluster. After giving the phase diagrams, the effect of the crystal field and anisotropy in the exchange interaction on the hysteresis loops have been determined. One important finding is double hysteresis loop behavior of the system in the low temperature and negative crystal field region, which disappears with the decreasing anisotropy in the exchange interaction. This behavior was carefully investigated and physical explanation has also been given.

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.

Dynamic behavior of a quantum Heisenberg ferromagnet in the presence of a periodically oscillating magnetic field has been analyzed by means of the effective field theory with two spin cluster. The dynamic equation of motion has been constructed with the help of a Glauber type stochastic process and solved for a simple cubic lattice. After the phase diagrams given, the behavior of the hysteresis loop area, coercive field and remanent magnetization with the anisotropy in the exchange interaction has been investigated in detail. Especially, by comparing of the magnitudes of the hysteresis loop area in the high anisotropy limit (i.e. Ising model) and low anisotropy limit (i.e. isotropic Heisenberg model), detailed description of the hysteresis loop area with the anisotropy in the exchange interaction given. Some interesting features have been obtained about this behavior as well as in phase diagrams such as tricritical points.

The effects of the bimodal random field distribution on the thermal and magnetic properties of of the Heisenberg thin film have been investigated by making use of a two spin cluster with the decoupling approximation. Particular attention has been devoted to the obtaining of phase diagrams and magnetization behaviors. The physical behaviors of special as well as tricritical points are discussed for a wide range of selected Hamiltonian parameters. For example, it is found that when the strength of magnetic field increases, the locations of special point in related plane decrease. Moreover, tricritical behavior has been obtained for the higher values of the magnetic field, and influences of the varying Hamiltonian parameters on its behavior have been elucidated in detail in order to have a better understanding of mechanism underlying of the considered system., Comment: arXiv admin note: text overlap with arXiv:1304.5552

The effect of the anisotropy in the exchange interaction on the critical temperature and the order parameter of the anisotropic Heisenberg model on a core-shell structured nanotube geometry has been investigated. As a formulation, effective field theory with the differential operator technique and decoupling approximation within the 4-spin cluster (EFT-4) has been used. The variation of the critical temperature with the anisotropy in the exchange interaction has been obtained. Besides, suitability of the effective field theory in small clusters as a formulation for the Heisenberg nanotube has been discussed and it is concluded that minimum size of the cluster is 4-spin cluster, which can give the correct critical description of the system.

The effect of the anisotropy in the exchange interaction on the phase diagrams and magnetization behavior of the Heisenberg thin film has been investigated with effective field formulation in a two spin cluster using the decoupling approximation. Phase diagrams and magnetization behaviors have been obtained for several different cases, by grouping the systems in accordance with, whether the surfaces/interior of the film have anisotropic exchange interaction or not. Particular attention has been paid on the evolution of the special point coordinate with the anisotropy in the exchange interaction. It has been concluded that for increasing ratio of the anisotropies in the exchange interaction between the surface and interior of the film, special point disappears at a special value of this ratio., Comment: 15 pages, 7 figures. arXiv admin note: text overlap with arXiv:1209.3952

In order to elucidate the important characteristics of hysteretic response, such as types of the frequency dispersion curves, the decay of hysteresis loop area, the mechanism of domain nucleation and/or growth in the dynamic process, etc., a followup examination after the original work has been presented. The additive complementary treatment is essentially based on the results of recent preprint arXiv:1302.2727 concerning the effect of oscillatory perturbation on the surface enhancement phenomenon in magnetic thin films. Throughout the analysis, the best appropriate parameter values have been chosen since they would allow us to achieve striking results. The topology of the response for different layer indices in two regimes of modified surface exchange has been particularly emphasized., Comment: 8 pages, 4 figures. arXiv admin note: text overlap with arXiv:1302.2727

The stationary state solutions of the Ising-type thin films with different layers in the presence of an external oscillatory field have been examined within the effective field theory. The exhibition focuses on understanding of the external field frequency and amplitude effect on the overall behavior of system for several powerful treatments. The particular attention has been paid on the dynamical parametric evolution of the special point at which the critical temperature of the three-dimensional infinite bulk system, where the surface and the modified exchange parameter are of no importance. Important characteristics of the films, such as surface enhancement phenomenon, effect of thickness on the dynamic process etc. have been introduced together with well known other characteristics. An attempt has been made to explain the relations between the competing time scales (intrinsic microscopic relaxation time of the system and the time period of the external oscillatory field) and frequency dispersion of the critical temperature coordinate of the special point., Comment: 13 pages, 7 figures. arXiv admin note: text overlap with arXiv:1206.5425

Effect of Gaussian random magnetic field distribution which is centered at zero on the phase transition properties of isotropic quantum Heisenberg model has been investigated on two (2D) and three dimensional (3D) lattices within the framework of effective field theory (EFT) for a two spin cluster (which is abbreviated as EFT-2). Beside the phase diagrams and the evolution of the magnetization versus temperature curves with the Gaussian magnetic field distribution width, critical Gaussian distribution width values, which make the critical temperature zero, have been obtained for several lattices. Moreover, it has been concluded that all critical temperatures are of the second order and reentrant behavior does not exist in the phase diagrams., Comment: 9 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1211.0893

Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigation has been made on a honeycomb lattice. Some interesting results, such as second order reentrant phenomena in the phase diagrams have been found., Comment: 11 pages, 5 figures. arXiv admin note: text overlap with arXiv:1211.0893

The effect of the anisotropy in the exchange interaction on the hysteresis loops within the anisotropic quantum Heisenberg model has been investigated with the effective field theory for two spin cluster. Particular attention has been devoted on the behavior of the hysteresis loop area, coercive field and remanent magnetization with the anisotropy in the exchange interaction for both ferromagnetic and paramagnetic phases., Comment: 10 pages, 6 figures

Effect of the trimodal random magnetic field distribution on the phase diagrams of the anisotropic quantum Heisenberg model has been investigated for three dimensional lattices with effective field theory (EFT) for a two spin cluster. Variation of the phase diagrams with the random magnetic field distribution parameters has been obtained and the effect of the anisotropy in the exchange interaction on the phase diagrams has been investigated in detail. Particular attention has been devoted on the behavior of the tricritical points with random magnetic field distribution., Comment: 8 pages, 4 figures

The effect of the zero centered Gaussian random magnetic field distribution on the phase diagrams and ground state magnetizations of the transverse Ising thin film has been investigated. As a formulation, the differential operator technique and decoupling approximation within the effective field theory has been used. The variation of the phase diagrams with the Gaussian distribution width (\sigma) has been obtained and particular attention has been paid on the evolution of the special point coordinate with distribution parameter. In addition, the ground state longitudinal and transverse magnetization behaviors have been investigated in detail., Comment: 23 pages, 9 figures

The decay of the hysteresis loop area of the system, which is obeying a site diluted kinetic Ising model, is considered by the disorder parameter using the effective field theory analysis. The exhibition focuses on the understanding of external field frequency, amplitude and the site concentration dependency of the hysteresis loop area for several powerful treatments. Important characteristics of the hysteretic response, such as frequency dispersion, effect of domain nucleation phenomenon on the dynamic process etc. has been introduced together with well known other characteristics. An attempt has been made to explain the relations between the competing time scales (intrinsic microscopic relaxation time of the system and the time period of the external oscillatory field) and the shape of the response. As a result of the detailed investigations, existence of essentially three, particularly four types of dispersion curves have been propounded., Comment: 16 pages, 8 figures

A cylindrical magnetic nanowire system composed of ferromagnetic core and shell layers has been investigated by using effective field theory with correlations. Both ferromagnetic and antiferromagnetic exchange couplings at the core-shell interface have been considered. Main attention has been focused on the effects of the quenched disordered shell bonds, as well as interface bonds on the magnetic properties of the system. A complete picture of the phase diagrams and magnetization profiles has been represented. It has been shown that for the antiferromagnetic nanowire system, the magnetization curves can be classified according to N\'{e}el theory of ferrimagnetism and it has been found that under certain conditions, the magnetization profiles may exhibit Q-type, P-type, N-type and L-type behaviors. The observed L-type behavior has not been reported in the literature before for the equilibrium properties of nanoscaled magnets. As another interesting feature of the system, it has been found that a compensation point can be induced by a bond dilution process in the surface. Furthermore, we have not found any evidence of neither the first order phase transition characteristics, nor the reentrance phenomena., Comment: 13 pages, 14 figures

The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of the Ising nanowire has been investigated with effective field theory with correlations. Gaussian distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as disappearance of the reentrant behavior and first order transitions which appear in the case of discrete distributions. Also for single and double Gaussian distributions, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system., Comment: 13 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1205.3219

The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of the Ising nanowire is investigated with effective field theory with correlations. Trimodal distribution chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters obtained and some interesting results found such as reentrant behavior. Also for the trimodal distribution, ground state magnetizations for different distribution parameters determined which can be regarded as separate partially ordered phases of the system., Comment: 15 pages, 8 figures

Nonequilibrium behavior and dynamic phase transition properties of a kinetic Ising model under the influence of periodically oscillating random-fields have been analyzed within the framework of effective field theory (EFT) based on a decoupling approximation (DA). Dynamic equation of motion has been solved for a simple cubic lattice ($q=6$) by utilizing a Glauber type stochastic process. Amplitude of the sinusoidally oscillating magnetic field is randomly distributed on the lattice sites according to bimodal and trimodal distribution functions. For a bimodal type of amplitude distribution, it is found in the high frequency regime that the dynamic phase diagrams of the system in temperature versus field amplitude plane resemble the corresponding phase diagrams of pure kinetic Ising model. Our numerical results indicate that for a bimodal distribution, both in the low and high frequency regimes, the dynamic phase diagrams always exhibit a coexistence region in which the stationary state (ferro or para) of the system is completely dependent on the initial conditions whereas for a trimodal distribution, coexistence region disappears depending on the values of system parameters., Comment: 11 pages, 11 figures

An improved unified formulation based on the effective field theory is introduced for a spin-1 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the multi-spin correlations systematically in a representative manner, as well as its single site counterparts in the system and gives much better results for critical temperature, in comparison with the other works in the literature. The formulation can be easily used to various kinds of spin-1 Ising models, as long as the system contains only the nearest neighbor interactions as spin-spin interactions., Comment: 23 pages, 6 figures

An improved unified formulation based on the effective field theory is introduced for a spin-1/2 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the multi-spin correlations systematically in a representative manner, as well as its single site counterparts in the system and gives results for the critical temperature of the system much better than those of the other works in the literature. The formulation can be easily applied to various extensions of s-1/2 Ising models, as long as the system contains only the nearest neighbor interactions as spin-spin interactions., Comment: 12 pages, 4 figures

Site diluted spin-1/2 Ising and spin-1 Blume Capel (BC) models in the presence of transverse field interactions are examined by introducing an effective-field approximation that takes into account the multi-site correlations in the cluster of a considered lattice with an improved configurational averaging technique. The critical concentration below which the transition temperature reduces to zero is determined for both models, and the estimated values are compared with those obtained by the other methods in the literature. It is found that diluting the lattice sites by non magnetic atoms may cause some drastic changes on some of the characteristic features of the model. Particular attention has been paid on the global phase diagrams of a spin-1 BC model, and it has also been shown that the conditions for the occurrence of a second order reentrance in the system is rather complicated, since the existence or extinction of reentrance is rather sensitive to the competing effects between D/J, \Omega/J and c., Comment: 19 pages, 14 figures

A spin-1 Blume-Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in $k_{B}T_{c}/J-D/J$ plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters $D/J$ and $\triangle/J$ on the phase diagrams of the system. The system exhibits clear distinctions in qualitative manner with coordination number $q$ for random crystal fields with $\triangle/J,D/J\neq0$. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions., Comment: 19 pages, 17 figures

Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. Random field distribution shape dependencies of the phase diagrams and magnetization curves are investigated for simple cubic, body centered and face centered cubic lattices. The conditions for the occurrence of reentrant behavior and tricritical points on the system are also discussed in detail., Comment: 13 pages, 8 figures

Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. Random field distribution shape dependence of the phase diagrams, magnetization and internal energy is investigated for a honeycomb lattice with a coordination number q=3. The conditions for the occurrence of reentrant behavior and tricritical points on the system are also discussed in detail., Comment: 7 pages, 9 figures