Bicritical Behavior Research Articles

Multi-magnetic phases in Fe 1−xNi xTa 2O 6

X-ray, neutron diffraction and magnetic susceptibility are reported for Fe x Ni 1− x Ta 2O 6 mixed oxides. X-ray refinement indicates homogeneous samples for all the reported concentrations. The neutron-diffraction measurements reveal magnetic structures with double propagation vectors. This system exhibits at least two bicritical points at about x=0.15 and 0.60. For these concentrations, at low temperatures, the system shows the coexistence of two magnetic structures. This bicritical behaviour is interpreted as induced by competition between the different magnetic structures.

X-ray diffraction and magnetic susceptibility measurements forFexNi1−xTa2O6

The trirutile family of the tapiolite-like compoundFexNi1−xTa2O6 was investigated by means of x-ray powder diffraction (XRD) and magnetic susceptibilitymeasurements. From Rietveld refinement it is demonstrated that the family is ahomogeneous solid solution obeying Vegard’s law. Magnetic susceptibility curves exhibittypical signatures of low-dimensional systems, with broadened maxima due to short rangecorrelations immediately above the antiferromagnetic transition temperatureTN.The T versus x phase diagram presents a minimum that suggests bicritical behaviour.

A theoretical study of magnetic phase transitions in ultra-thin films: Application to NiO

Phase diagrams and critical temperatures of { H Ising = - 1 / 2 J d ∑ i , j nn S i S j + 1 / 2 J se ∑ i , j nnn S i S j } projected onto fcc (1 0 0) layers, which is believed to be applicable to first-row transition metal oxides such as VO, MnO and NiO, are obtained from mean field theory and Monte Carlo simulations. Within the regime, J se > 0, which includes MnO and NiO, both approaches predict bicritical behaviour of the AF 2 and AF 3 antiferromagnetic spin alignments for odd numbers of layers greater than one and monocritical behaviour for even numbers of layers, even when films are described by single values of J d and J se. The ferromagnetic alignment, on the other hand, exhibits monocritical behaviour for all thicknesses from the monolayer through to the bulk. For values of ( x = J d/ J se) which are close to those obtained from first principles calculations for NiO and also those derived from measured magnon spectra, estimates of the thickness dependence of the critical temperature from Monte Carlo simulations are similar to that derived from linear polarised X-ray absorption spectra of NiO(1 0 0) ultra-thin films grown epitaxially on MgO(1 0 0) [D. Alders, L.H. Tjeng, F.C. Voogt, T. Hibma, G.A. Sawatzky, J. Vogel, M. Sacchi, S. Iacobucci, Phys. Rev. B 57 (1998) 11623].

Multiparameter Critical Situations, Universality and Scaling in Two-Dimensional Period-Doubling Maps

We review critical situations, linked with period-doubling transition to chaos, which require using at least two-dimensional maps as models representing the universality classes. Each of them corresponds to a saddle solution of the two-dimensional generalization of Feigenbaum-Cvitanovic equation and is characterized by a set of distinct universal constants analogous to Feigenbaum’s α and δ. One type of criticality designated H was discovered by several authors in 80-th in the context of period doubling in conservative dynamics, but occurs as well in dissipative dynamics, as a phenomenon of codimension 2. Second is bicritical behavior, which takes place in systems allowing decomposition onto two dissipative period-doubling subsystems, each of which is brought by parameter tuning onto a threshold of chaos. Types of criticality designated as FQ and C occur in non-invertible two-dimensional maps. We present and discuss a number of realistic systems manifesting those types of critical behavior and point out some relevant conditions of their potential observation in physical systems. In particular, we indicate a possibility for realization of the H type criticality without vanishing dissipation, but with its compensation in a self-oscillatory system. Next, we present a number of examples (coupled Henon-like maps, coupled driven oscillators, coupled chaotic self-oscillators), which manifest bicritical behavior. For FQ-type we indicate possibility to arrange it in non-symmetric systems of coupled period-doubling subsystems, e.g. in Henon-like maps and in Chua’s circuits. For C-type we present examples of its appearance in a driven Rossler oscillator at the period-doubling accumulation on the edge of syncronization tongue and in a model map with the Neimark–Sacker bifurcation

Randomness effect on multicritical phenomena in double-exchange systems

Double-exchange model interacting with adiabatic phonons is studied in the presence of randomness by using the Monte-Carlo method and the systematic size-scaling analysis. A bicritical behavior is found between the ferromagnetic metal and the charge-ordered insulator. We find the distinct response to the randomness between these two states, which agrees well with the experimental results in the colossal magnetoresistance manganites.

Bicriticality in FexCo1-xTa2O6.

X-ray and neutron-diffraction, dc magnetic susceptibility, magnetization, and specific-heat measurements are reported for FexCo(1-x)Ta2O6 mixed oxides. X-ray refinement indicates homogeneous samples for all the reported concentrations. The neutron-diffraction measurements reveal magnetic structures with double propagation vectors (+/-1/4,1/4,1/4) for CoTa2O6, and (1/2,0,1/2) and (0,1/2,1/2) for FeTa2O6. The latter remain unchanged in the Fe-rich samples, for 0.46< or =x<1.00, while the Co-rich samples show propagation vectors (+/-1/4,1/4,0) for 0.09< or =x<0.46. The temperature vs x phase diagram exhibits a bicritical point at about T=4.9 K and x=0.46. For this concentration, and at low temperatures, the system shows coexistence of both magnetic structures. This novel bicritical behavior is interpreted as induced by competition between the different magnetic and crystallographic structures.

Influence of striction effects on the multicritical behavior of homogeneous systems

A field-theoretical description of the behavior of homogeneous, elastically isotropic, compressible systems characterized by two order parameters at the bicritical and tetracritical points is presented. For three-dimensional Ising-like systems, a similar description is performed in the two-loop approximation in three dimensions with the use of the Padé-Borel summation technique. The renormalization group equations are analyzed, and fixed points corresponding to different types of multicritical behavior are determined. It is shown that the effect of elastic strains causes a change from a bicritical behavior to a tetracritical one and leads to the appearance of a wide variety of multicritical points.

Scaling properties of bicritical dynamics in unidirectionally coupled period-doubling systems in the presence of noise.

We study scaling regularities associated with the effects of additive noise on the bicritical behavior of a system of two unidirectionally coupled quadratic maps. A renormalization group analysis of the effects of noise is developed. We outline the qualitative and quantitative differences between the response of the system to random perturbations added to the master subsystem or the slave subsystem. The universal constants determining the rescaling rules for the intensity of the noise sources in the master and slave subsystems are found to be gamma=6.619036... and nu=2.713708..., respectively. A number of computer graphical illustrations for the scaling regularities is presented. We discuss the smearing of the fine structure of the bicritical attractor and the Fourier spectra in the presence of noise, the self-similar structure of the Lyapunov charts on the parameter plane near the bicritical point, and the shift of the threshold of hyperchaos in dependence of the noise intensity.

Universal Bicritical Behavior of Period Doublings in Unidirectionally Coupled Oscillators

We study the bicritical behavior of period doublings in unidirectionally coupled oscillators to confirm the universality of the bicriticality in an abstract system of two unidirectionally coupled one-dimensional (1D) maps. A transition to hyperchaos occurs (i.e., a hyperchaotic attractor with two positive Lyapunov exponents appears) when crossing a bicritical point where two Feigenbaum critical lines of a period-doubling transition to chaos in the two subsystems meet. Using both a “residue-matching” renormalization group method and a direct numerical method, we make an analysis of the scaling behavior near the bicritical point. It is thus found that the second response subsystem exhibits a new type of non-Feigenbaum critical behavior, while the first drive subsystem is in the usual Feigenbaum critical state. Note that the bicritical scaling behavior is the same as that in the unidirectionally coupled 1D maps. We thus suppose that bicriticality may be observed generally in real systems, consisting of period-doubling subsystems with a unidirectional coupling.

Bicritical scaling behavior in unidirectionally coupled oscillators.

We study the scaling behavior of period doublings in a system of two unidirectionally coupled parametrically forced pendulums near a bicritical point where two critical lines of period-doubling transition to chaos in both subsystems meet. When crossing a bicritical point, a hyperchaotic attractor with two positive Lyapunov exponents appears, i.e., a transition to hyperchaos occurs. Varying the control parameters of the two subsystems, the unidirectionally coupled parametrically forced pendulums exhibit multiple period-doubling transitions to hyperchaos. For each transition to hyperchaos, using both a "residue-matching" renormalization group method and a direct numerical method, we make an analysis of the bicritical scaling behavior. It is thus found that the second response subsystem exhibits a new type of non-Feigenbaum scaling behavior, while the first drive subsystem is in the usual Feigenbaum critical state. The universality of the bicriticality is also examined for several different types of unidirectional couplings.

Bicritical behavior of period doublings in unidirectionally coupled maps.

We study the scaling behavior of period doublings in two unidirectionally coupled one-dimensional maps near a bicritical point where two critical lines of period-doubling transition to chaos in both subsystems meet. Note that the bicritical point corresponds to a border of chaos in both subsystems. For this bicritical case, the second response subsystem exhibits a type of non-Feigenbaum critical behavior, while the first drive subsystem is in the Feigenbaum critical state. Using two different methods, we make the renormalization-group analysis of the bicritical behavior and find the corresponding fixed point of the renormalization transformation with two relevant eigenvalues. The scaling factors obtained by the renormalization-group analysis agree well with those obtained by a direct numerical method.

Adsorption of a macromolecule in an external field: An exactly solvable model with bicritical behavior

We introduce a model of an adsorbing polymer chain in an external field, which admits exact analytical solution for the partition function for a finite number of the units, $N.$ In the thermodynamic limit, the system has an isotropic and two ordered phases, exhibits continuous and discontinuous phase transitions, and has a bicritical point. We obtain exact expressions for the Landau free energy as a function of an order parameter in the vicinity of the first- and second-order phase transition lines, and compare them to the original theory. The Landau free energy is also calculated as a function of two independent order parameters in the vicinity of the bicritical point. The distribution of complex zeros of the partition function is found for both first- and second-order transitions. In the thermodynamic limit it is described by exact analytical expressions, allowing a comparison to the existing phenomenological results within the framework of the Yang-Lee-Fisher approach. An advantage of the model presented is that the partition function can be calculated analytically not only in the thermodynamic limit, but for finite $N$ as well. The ideas of finite-size scaling analysis are checked against the exact solution, in terms of both the functional form of the free energy and the $N$ dependence of the distribution of Fisher zeros.

Superpositions of multifractals: Generators of phase transitions in the generalized thermodynamic formalism

We investigate the superposition of multifractals in the generalized thermodynamic formalism. It is shown analytically that phase transitions of first and second order are obtained and that the topology of the corresponding critical lines endows bicritical behavior. We demonstrate that these phase transitions can be observed in the spectrum of fractal dimensions and in the spectra of related quantities. Therefore, the obtained results are of importance for the interpretation of experimental systems.

MULTI-PARAMETER CRITICALITY IN CHUA'S CIRCUIT AT PERIOD-DOUBLING TRANSITION TO CHAOS

Investigation of non-Feigenbaum types of period-doubling universality is undertaken for a single Chua's circuit and for two systems with a unidirectional coupling. Some codimension-2 critical situations are found numerically that were known earlier for bimodal 1D maps. However, the simplest of them (tricritical) does not survive in a strict sense when the exact dynamical equations are used instead of the 1D map approximation. In coupled systems double Feigenbaum's point and bicritical behavior are found and studied. Scaling properties that are the same as in two logistic maps with a unidirectional coupling are illustrated.

Biquadratic exchange and critical behaviour in the diluted antiferromagnet EuxSr1−xTe

Magnetization, specific heat, magnetocaloric effect, and neutron diffraction measurements have been performed in order to better understand the magnetic interactions and phase transitions in the diluted antiferromagnetic system EuxSr1−xTe. Due to the low Neel temperature ofT N =9.8 K and the associated small critical field ofB C (T=0)=7.5 T, EuTe provides the opportunity to change the angle between the antiferromagnetic moments continuously between 180° and 0° by applying a magnetic field and allows thus to probe the type of the magnetic interaction. It is found that in addition to the common bilinear Heisenberg exchange mechanism there is evidence for a small biquadratic exchange term, which has important consequences on the critical behaviour of EuxSr1−xTe. In the case of EuTe the biquadratic exchange supports the antiferromagnetic order, such that virtually no anisotropy exists and this restricts the anti-Herromagnetic (AF) to spin-flop (SF) transition toB 0=0. On dilution with strontium, the biquadratic interaction decreases strongly and changes its sign at x≈0.83 thus favouring the perpendicular moment orientation. This acts like an anisotropy on the dominating antiferromagnetic bilinear interaction and shifts the AF-SF phase line to finite fields which reach values of 0.3 T forT→0. No bicritical behaviour is observed, but instead, the SF phase is the state of lowest energy in a small temperature interval belowT N . The critical exponent α(x) of the specific heat decreases in a non-linear way with dilution starting from a large positive value for EuTe. α(x) is close to the Heisenberg value −0.12 nearx≈0.83 where the biquadratic interaction is zero. The same applies for the exponent β of the sublattice magnetization.

Faraday-optical study of the tri-to-bicritical crossover in anisotropic heisenberg antiferromagnets Fe1-xNixCl2, 0.18 ≤x≤ 0.67

Abstract The magnetic phase diagrams, H-vs-T and M-vs-T, of solid solutions Fe1-x Ni x Cl2, 0.18 ≤ x ≤ 0.67, are investigated using Faraday rotation measurements. Bicritical behavior is observed for x > 0.57, whereas tricritical behavior is encountered for x < 0.57. In the low-x regime a critical end-point of an additional low-T second-order spin flop-to-paramagnetic phase boundary seems to emerge linearly with x. It coalesces with the tricritical point at x = 0.57, forming a “new multicritical point” of higher order as predicted by Galam and Aharony. This merges into the bicritical point in the high-x regime.

BICRITICAL DYNAMICS OF PERIOD-DOUBLING SYSTEMS WITH UNIDIRECTIONAL COUPLING

The simplest case of bicritical behavior arises in a system of two logistic maps with unidirectional coupling in the point of a parameter plane where lines of transition to chaos in both subsystems meet. We develop a renormalization group analysis of the bicriticality and find the corresponding fixed point universal function and constants featuring the scaling properties of the second system while the first one is in the Feigenbaum critical state. Fractal properties of the bicritical attractor and its quantitative characteristics (σ-functions, f(α)-spectra, generalized dimensions) are considered. It is shown that the bicriticality may be observed as well in lattice models of flow systems consisting of more than two coupled elements.

An experimental verification of a percolation model for RuO2-glass thick resistive films

The authors present results of their experimental work concerning the sheet resistance, RSquare Operator , temperature characteristics of resistance and relative power spectral density of 1/f noise, S, versus the volume fraction of conducting component, nu , for RuO2-glass composites. They eliminate the contributions of contact-film-resistive-film interfaces to the measured characteristics. The authors find that the composites investigated can be mapped onto the three-component 3D random resistor network (RRN) formed from well conducting metallic bonds, poorly conducting metal-insulator-metal (MIM) bonds and those not conducting. They provide the physical interpretation of the network's parameters: hg, hs, b1, i.e. the ratio of conductances of poorly and well conducting bonds, the ratio of their 1/f noise relative power spectral densities and the fraction of metallic bonds in the set of all conducting bonds, respectively. The electrical transport characteristics of RuO2-glass thick resistive films are interpreted with the help of bicritical behaviour of such a percolation network. They find qualitative agreement between S(RSquare Operator ) experimental data for a certain region of nu and that from 3D RRN simulations using the Monte Carlo real space renormalization group algorithm.

Pressure induced transitions between para-, heli- and ferromagnetic phases of Mn 0.61Cr 0.39As studied by neutron diffraction

The pressure-temperature phase diagram for Mn 0.61Cr 0.39As has been determined by powder neutron diffraction and ac magnetic susceptibility measurements for pressures up to 10 kbar. Three magnetically ordered phases, ▪ ferro- (F) and two helimagnetic (H a and H c), together with a paramagnetic (P) phase prevail at different pressure and temperature conditions. The bicritical behaviour of the H c, F, P triple point is discussed. Data are presented for the temperature and pressure dependences of the propagation vector of the (modulated) H c magnetic structure , and primarily compressibility data are given at 225 K.

The effects of random fields on the critical and bicritical behavior of Mn x Zn1?x F2

We have carried out a comprehensive study of the static and dynamic spin-spin correlations of Mn x Zn1−xF2 in a magnetic field. Samples withx=0.75 andx=0.5 have been studied. This system exhibits behavior closely related, if not identical, to that of the Random Field Ising Model (RFIM). An additional feature of Mn x Zn1−xF2 is that it exhibits an easily accessible bicritical point; thus one can study the changeover from the RFIM to the uniformXY model with a transverse random field. Quite generally, the instantaneous spin-spin correlations in a field are described by a combination of Lorentzian, Lorentzian-squared and delta function terms the latter corresponds to the long range order (LRO) component. In the Ising phase one finds history dependent behavior as discussed previously. In theXY phase, except very near the spin-flop boundary, one finds ergodic behavior withXY LRO and Lorentzian squared Ising fluctuations. Rather complicated instability effects are found all along the spin-flop boundary. Further, when one establishes LRO in theXY phase and lowers the field through the spin-flop value, one obtains a LRO Ising state in thex=0.75 sample whereas one obtains the field-cooled domain state in thex=0.50 sample. This dramatic difference in behavior is not understood. Our results on the RFIM aspects of the problem are consistent with our previous studies. The transition is dominated by the metastability effects with an underlying equilibrium transition which is either first order or weakly second order (β≈0). The underlying transition manifests itself directly in measurements of the dynamic response nearT N (H). From the data above the metastability boundary we deduce for the static correlation length exponentv=1.4±0.3 in good agreement with theory. We find for the RFIM crossover exponent φRF=1.5±0.2 where the errors represent the spread in values obtained from different techniques. Finally, we have determined in detail the field-temperature phase diagram of thex=0.5 sample including the critical behavior along the spin-flop line; the latter transition appears to be second order for an extended region.