Bayram Deviren

Topology of the correlation networks among major currencies using hierarchical structure methods

We studied the topology of correlation networks among 34 major currencies using the concept of a minimal spanning tree and hierarchical tree for the full years of 2007–2008 when major economic turbulence occurred. We used the USD (US Dollar) and the TL (Turkish Lira) as numeraires in which the USD was the major currency and the TL was the minor currency. We derived a hierarchical organization and constructed minimal spanning trees (MSTs) and hierarchical trees (HTs) for the full years of 2007, 2008 and for the 2007–2008 period. We performed a technique to associate a value of reliability to the links of MSTs and HTs by using bootstrap replicas of data. We also used the average linkage cluster analysis for obtaining the hierarchical trees in the case of the TL as the numeraire. These trees are useful tools for understanding and detecting the global structure, taxonomy and hierarchy in financial data. We illustrated how the minimal spanning trees and their related hierarchical trees developed over a period of time. From these trees we identified different clusters of currencies according to their proximity and economic ties. The clustered structure of the currencies and the key currency in each cluster were obtained and we found that the clusters matched nicely with the geographical regions of corresponding countries in the world such as Asia or Europe. As expected the key currencies were generally those showing major economic activity.

Dynamic magnetizations and dynamic phase transitions in a transverse cylindrical Ising nanowire

In this paper, we extend the paper of Kaneyoshi (2010 J. Magn. Magn. Mater. 322 3410–5) to investigate the dynamic magnetizations and dynamic phase transitions of a transverse cylindrical Ising nanowire system by using the effective field theory with correlations and the Glauber-type stochastic dynamics under a time-dependent oscillating external magnetic field. The dynamic effective field equations for the average longitudinal and transverse magnetizations on the surface shell and core are derived by using the Glauber transition rates. Temperature dependences of the dynamic longitudinal magnetizations, the transverse magnetizations and the total magnetizations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as the dynamic phase transition temperatures and the compensation behaviors. The system is strongly affected by the surface situations. Some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and the core. According to the values of Hamiltonian parameters, four different types of compensation behaviors in the Neel classification nomenclature exist in the system. The results are compared with some theoretical works and good overall agreement is observed.

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

Abstract We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, σ = ± 1 2 , alternated with spins that can take the four values, S = ± 3 2 , ± 1 2 . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.

The effective-field study of a mixed spin-1 and spin-5/2 Ising ferrimagnetic system

An effective-field theory with correlations is developed for a mixed spin-1 and spin-5/2 Ising ferrimagnetic system on the honeycomb ( = 3) and square ( = 4) lattices in the absence and presence of a longitudinal magnetic field. The ground-state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (1) plane. We also investigate the thermal variations of the sublattice magnetizations, and present the phase diagrams in the (1/|J|,kBT/|J|) plane. The susceptibility, internal energy and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the absence and presence of the applied longitudinal magnetic field. Moreover, the system undergoes second- and first-order phase transition; hence, the system gives a tricritical point. The system also exhibits reentrant behavior.

Dynamic phase transition in the kinetic spin-3/2 Blume–Emery–Griffiths model in an oscillating field

The dynamic phase transitions are studied, within a mean-field approach, in the kinetic Blume–Emery–Griffiths model under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The behaviour of the time-dependence of the order parameters and the behaviour of the average order parameters in a period, which is also called the dynamic order parameters, as a function of reduced temperature, are investigated. The nature (continuous and discontinuous) of transition is characterized by studying the average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The phase diagrams exhibit one, two, or three dynamic tricritical points and a dynamic double critical end point, and besides a disordered and two ordered phases, seven coexistence phase regions exist, which strongly depend on interaction parameters. We also calculate the Liapunov exponent to verify the stability of solutions and the dynamic phase transition points.

Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (ω) and static external field amplitude (h0) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ω and h0.

Dynamic Compensation Temperature in the Mixed Spin-1/2 and Spin-3/2 Ising Model in an Oscillating Field on Alternate Layers of Hexagonal Lattice

The dynamic behavior of a mixed spin-1/2 and spin-3/2 Ising model with a crystal-field interaction in the presence of a time-varying magnetic field on alternate layers of hexagonal lattice is studied by using the Glauber-type stochastic dynamics. We study time variations of the average magnetizations in order to find the phases in the systems, and the temperature dependence of the dynamic sublattice magnetizations and total magnetization to obtain the dynamic phase transition (DPT) points and dynamic compensation points, respectively, as well as to characterize the nature (continuous and discontinuous) of transitions. Dynamic phase diagrams are also calculated for both DPT points and dynamic compensation effects. According to values of Hamiltonian parameters, besides the paramagnetic (p), antiferromagnetic (af) and antiferrimagnetic (i) fundamental phases, the af+p, i+p and i+af mixed phases, and the compensation temperature or P- and L-types behavior in the Neel classification nomenclature exist in the system.

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point (TP), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Neel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.

Critical behavior of a mixed ferrimagnetic ternary alloy on the Bethe lattice

The critical behavior of the mixed Ising model of the type ABpC1−p ternary alloy consisting of spins σ = 1/2, S = 1, and m = 3/2 is investigated on the Bethe lattice by using the exact recursion relations. The exact expressions for the magnetizations and magnetic susceptibilities are found, and the thermal behaviors of the magnetizations and susceptibilities are studied. The magnetizations and susceptibilities have also been investigated as functions of the crystal-field interaction or single-ion anisotropy. The phase diagram has been constructed according to which the system always undergoes a second-order phase transition for the coordination number q ≤ 3 and second-and first-order phase transitions for q > 3; hence, the system has a tricritical point. The system also exhibits reentrant behaviors.

Hierarchical structure of the European countries based on debts as a percentage of GDP during the 2000-2011 period

We investigate hierarchical structures of the European countries by using debt as a percentage of Gross Domestic Product (GDP) of the countries as they change over a certain period of time. We obtain the topological properties among the countries based on debt as a percentage of GDP of European countries over the period 2000–2011 by using the concept of hierarchical structure methods (minimal spanning tree, (MST) and hierarchical tree, (HT)). This period is also divided into two sub-periods related to 2004 enlargement of the European Union, namely 2000–2004 and 2005–2011, in order to test various time-window and observe the temporal evolution. The bootstrap techniques is applied to see a value of statistical reliability of the links of the MSTs and HTs. The clustering linkage procedure is also used to observe the cluster structure more clearly. From the structural topologies of these trees, we identify different clusters of countries according to their level of debts. Our results show that by the debt crisis, the less and most affected Eurozone’s economies are formed as a cluster with each other in the MSTs and hierarchical trees.