Correlation radius of polarization fluctuations in the disordered ferroelectrics

Random field effects on the anisotropic quantum Heisenberg model with Gaussian random magnetic field distribution

Effects of the randomly distributed magnetic field on the phase diagrams of Ising nanowire I: Discrete distributions

We extend the self-consistent Ornstein–Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the random field Ising model. Within the replica formalism, we treat the quenched random field just as another spin variable, thereby avoiding the usual average over the random field distribution. This allows us to study the influence of the distribution on the phase diagram in finite dimensions. The thermodynamics and the correlation functions are obtained as solutions of a set a coupled partial differential equations with magnetization, temperature, and disorder strength as independent variables. A preliminary analysis based on high-temperature and 1/d series expansions shows that the theory can predict accurately the dependence of the critical temperature on disorder strength (no sharp transition, however, occurs for d≤4). For the bimodal distribution, we find a tricritical point which moves to weaker fields as the dimension is reduced. For the Gaussian distribution, a tricritical point may appear for d around 4.

Purpose The assembly accuracy of large thin-walled structures is hard to be predicted due to the random field distribution of initial deviations. This paper aims to propose a new shape characterization and assembled accuracy analysis method for large thin-walled structures with random continuous field deviation. Design/methodology/approach In this paper, the random field deviation is described by the basic deviation patterns and corresponding deviation coefficients. The ranges of deviation coefficients for random field deviations are derived by the fluctuation ranges of initial deviations. The assembled geometrical accuracy indexes are calculated. A surrogate model for the prediction of assembled geometrical accuracy is constructed based on neural network method. The mapping correlation of part deviation coefficients and geometrical accuracy of assembly is established and the fluctuation of geometrical accuracy for assembled thin-walled structure is obtained. Findings The assembling process of two cylindrical panels is analyzed theoretically and experimentally, by which the method of field deviation characterization and assembled accuracy analysis is verified. The statistical distribution of assembled accuracy with random initial field deviation is obtained. The assembled accuracy indexes can be predicted rapidly with given initial deviation. Originality/value A new characterization method for random field deviation is proposed for large thin-walled structures, and the fluctuation ranges of accuracy indexes for assembly can be obtained efficiently with that of parts, which is the premise of assemblability evaluation and deviation control for large thin-walled structures.

We study the thermodynamic properties of random transverse field mixed spin system in the presence of single-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, the detailed phase diagrams are described and some interesting results are found under trimodal random transverse field distribution. A small single-ion anisotropy can magnify magnetic ordering region at low temperatures and existence of a large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phase transitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodal transverse field distribution.

For pt. I, see ibid., vol.5, 3397 (1972). The shape of APR lines from (3d)4 ions in Al2O3 has been investigated when the direction of the applied magnetic field and constant electric fields up to 70 kV cm-1 are varied. It is found that the spectrum is much more sensitive to an electric field applied along the a axis than the same field along the b axis. A detailed semiquantitative discussion of the intensities of the edges and peaks in the spectrum is given. From the results, information is obtained on the E type components of the random internal strains and electric field distributions experienced by the Cr2+ and Mn3+ ion impurities in Al2O3.

We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent gamma. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for gamma<3. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for gamma>3. The phase transition may be either continuous or discontinuous depending on the shape of the random field distribution. We derive the condition for the nature of the phase transition. Numerical simulations are performed to confirm the results.

The paper is devoted to the recent developments and extensions of the transionospheric stochastic channel model developed by the authors. The Hybrid Scintillation Propagation Model (HSPM) [1] was created as the combination of the Complex Phase Method (CPM) and rigorous technique of the random (not necessarily phase) screen. The CPM, in turn, is the extension of the classic Rytov's method to the case of the inhomogeneous background medium. In order to correctly describe the special case when the propagation path is oriented close to the direction of the magnetic field lines, i.e., along the strongly elongated ionospheric irregularities, the CPM was extended in [2] to account for the highly anisotropic character of the ionospheric turbulence. Another extension concerns accounting the second order term in the expansion of the complex phase method employed in CPM. The effect is that, in distinction from the commonly accepted Gaussian distribution of the complex phase in the first order approximation, the accounting of the second order term produces the deviation of the distribution from the Gaussianity. The main effects are the shift of the mean and skewness of the probability density function of the log-amplitude distribution after passing the turbulent layer. These effects can be quantitatively characterized utilizing the higher cumulants of the distribution that are derived employing the second order terms of the complex phase expansion [3]. In particular, the third cumulant characterizes the skewness of the distribution. This distribution is then utilized in the algorithm [4] of generating the corresponding non-Gaussian distribution of the random field realizations on the screen, introduced below the ionosphere according to the HSPM technique. The extensions mentioned lead to the random field distributions different of those obtained, if the effects of the anisotropy and deviation from Gaussianity were not properly taken into account. In turn, this finally results in the different field distribution and values of the scintillation indices for the random field observed on the Earth's surface. In the paper, the details of the analytical derivations and results of simulation making use of the extended HSPM model will be presented and discussed.

Stochastic wave field solution of the 2D elastic wave equation based on the random Fourier–Stieltjes increments

Accurate Rayleigh propagation environments within an ideal reverberation chamber (RC) are synthesized computationally using a superposition of plane-waves (PWs). Randomness in the electro-magnetic (EM) field distribution is achieved by synthesizing many field realizations featuring slant-polarized PWs with randomly defined transverse field components. These PWs propagate along a large number of predefined and uniformly distributed directions determined only once via an efficient spiraling sampling scheme over the unit sphere. Comparisons with theoretical Rayleigh field statistics indicate that the proposed method yields random EM field distributions that in several cases follow more closely the field spatial correlation properties, for comparable numerical burden, than other available numerical techniques. Finally, a formula relating the number of PWs to the size of a desired RC analysis volume was provided.

The dielectric constant and dielectric loss of pure NaCN, KCN, RbCN, and CsCN crystals has been comprehensively studied as a function of temperature. Besides dielectric measurements with a capacitance bridge in the 10 0 to 10 5 Hz regime, thermally stimulated depolarization current (TSDC) techniques have been used for the first time in these systems to obtain information about the reorientation and ordering behavior of CN - ions at lowest temperatures and relaxation rates. The extended dipolar reorientation data are analyzed, using either Cole-Cole or Havriliak-Negami distributions of relaxation times with temperature-dependent parameters. A phenomenological model is proposed, based on the assumed existence of a distribution of random bias electric fields to explain the observed behavior of the dipolar susceptibility in relation to CN- electric-dipole ordering in these systems.

We study the magnetization response of a frozen ferrofluid as large-diameter (10-nm) magnetite particles are added to a dilute, random distribution of small-diameter (5-nm) moments. The small dipole moments are free to relax down to low temperatures, while the large dipoles become immobilized when the solvent freezes, acting as a random local field. The glass transition temperature is a sensitive function of the random field concentration, permitting the investigation of the crossover from spin-glass to random-field behavior.

Lead-based perovskite relaxor ferroelectrics are widely used as materials for numerous applications due to their extraordinary dielectric, piezoelectric, and electrostrictive properties. While the mechanisms of relaxor behavior are disputable, the importance of quenched (static) random electric fields created at nanoscale by the disordered heterovalent cations has been well recognized. Meanwhile, an increasing amount of scientific and technological efforts has been concentrated on lead-free perovskites, in particular, solid solutions of classical ferroelectric $\mathrm{BaTi}{\mathrm{O}}_{3}$ (BT), which better meet ecological requirements. Among BT-based solutions the homovalent systems are elaborately studied where strong random electric fields are absent, while the solubility limit of heterovalent solutions is typically too low to fully reveal the peculiarities of relaxor behavior. In this paper, we prepare a perovskite solid solution system $(1\ensuremath{-}x)\mathrm{B}{\mathrm{a}}^{2+}\mathrm{T}{\mathrm{i}}^{4+}{\mathrm{O}}_{3}\ensuremath{-}x\mathrm{D}{\mathrm{y}}^{3+}\mathrm{F}{\mathrm{e}}^{3+}{\mathrm{O}}_{3}$ ($0\ensuremath{\le}x\ensuremath{\le}0.3$) and study it as a model heterovalent lead-free system. We determine crystal structure, ferroelectric, and dielectric properties of ceramics in a wide range of temperatures and concentrations, construct a phase diagram, and find and analyze the concentration-induced crossover from normal ferroelectric to relaxor behavior. We demonstrate that quenched random electric fields of moderate strength promote the ferroelectric-to-relaxor crossover, but do not change qualitatively the peculiarities of relaxor behavior, while strong enough fields destroy the relaxor state, so that the material becomes an ordinary linear dielectric. The experimental results are compared with the predictions of known theories of relaxor ferroelectricity.

Mixed alkanethiol monolayers on gold surfaces: Wetting and stability studies

We consider the zero-temperature single-spin-flip dynamics of the random-field Ising model on a Bethe lattice in the presence of an external field h. We derive the exact self-consistent equations to determine the distribution Prob(s) of avalanche sizes s, as the external field increases from large negative to positive values. We solve these equations explicitly for a rectangular distribution of the random fields for a linear chain and the Bethe lattice of coordination number z=3, and show that in these cases, Prob(s) decreases exponentially with s for large s for all h on the hysteresis loop. We found that for z >3 and for small disorder, the magnetization shows a first order discontinuity for several continuous and unimodel distributions of random fields. The avalanche distribution Prob(s) varies as s^{-3/2} for large s near the discontinuity.