The random field Ising model with an asymmetric trimodal probability distribution

The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(h_i)=pδ(h_i−h₀)+qδ(h_i+h₀)+rδ(h_i), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), h_i is the random field variable and h₀ the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of p,q and h₀, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h₀.     

The random field Ising model with an asymmetric and anisotropic trimodal probability distribution

The Ising model in the presence of a random field, drawn from the asymmetric and anisotropic trimodal probability distribution P(_hi)=pδ(_hi−_h0)+qδ(_hi+λ∗_h0)+rδ(_hi)$P\left(h_i\right)=p\delta (h_i-h_0)+q\delta (h_i+\lambda \ast h_0)+r\delta \left(h_i\right)$, is investigated. The partial probabilities p,q,r$p,q,r$ take on values within the interval [0,1]$[0,1]$ consistent with the constraint p+q+r=1$p+q+r=1$; asymmetric distribution, _hi$h_i$ is the random field variable with basic absolute value _h0$h_0$ (strength); λ$\lambda$ is the competition parameter, which is the ratio between the respective strength of the random magnetic field in the two principal directions (+z)$(+z)$ and (−z)$(-z)$ and is positive so that the random fields are competing, anisotropic distribution. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays mainly second order phase transitions, which, for some values of p,q$p,q$ and _h0$h_0$, are followed by first order phase transitions joined smoothly by a tricritical point; occasionally, two tricritical points appear implying another second order phase transition. In addition to these points, re-entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of λ$\lambda$, p$p$ and q$q$. Using the variational principle, we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to _h0$h_0$, considered as an independent variable in addition to the temperature.     

Multipole mixing ratios of transitions in Te

Gamma-gamma directional correlation measurements were made on nine transitions in ¹²⁴Te with a NaI(Tl)-Ge(Li) detector arrangement and multichannel analysis. The multipole mixing ratios obtained were δ(646) = 0.000±0.001, δ(714) = 1.5_−0.3^+0.6, δ(723) = −3.3±0.2, δ(1437) = 3.7_−2.0^+2.7, δ(1489) = −3.4_−1.5^+0.9, δ(968) = −0.03_−0.05^+0.06, δ(1368) = −0.045±0.090, δ(1045) = 0.041_−0.041^+0.047, δ(1691) = −0.02±0.01, and δ(2091) = 0.00_−0.03^+0.02. The first δ is M3/E2, the next three are E2/M1, and the last five are M2/E1. The retardation (a factor of approximately 50) of the crossover to cascade transitions from the 2039 keV, third 2⁺ level to the second and first 2⁺ levels is essentially the same for both the M1 and E2 components. In addition, spin and parity assignments of 2⁺ were made for the 2039 and 2092 keV levels.     

The transverse spin-1 Ising model with random interactions

The phase diagrams of the transverse spin-1 Ising model with random interactions are investigated using a new technique in the effective field theory that employs a probability distribution within the framework of the single-site cluster theory based on the use of exact Ising spin identities. A model is adopted in which the nearest-neighbor exchange couplings are independent random variables distributed according to the law P(J_ij)=pδ(J_ij−J)+(1−p)δ(J_ij−αJ). General formulae, applicable to lattices with coordination number N, are given. Numerical results are presented for a simple cubic lattice. The possible reentrant phenomenon displayed by the system due to the competitive effects between exchange interactions occurs for the appropriate range of the parameter α.     

Dynamic magnetic hysteresis behavior and dynamic phase transition in the spin-1 Blume-Capel model

The nature (time variation) of response magnetization m(wt) of the spin-1 Blume-Capel model in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We determine the time variations of m(wt) and h(wt) for various temperatures, and investigate the dynamic magnetic hysteresis behavior. We also investigate the temperature dependence of the dynamic magnetization, hysteresis loop area and correlation near the transition point in order to characterize the nature (first- or second-order) of the dynamic transitions as well as obtain the dynamic phase transition temperatures. The hysteresis loops are obtained for different reduced temperatures and we find that the areas of the loops are decreasing with the increasing of the reduced temperatures. We also present the dynamic phase diagrams and compare the results of the EFT with the results of the dynamic mean-field approximation. The phase diagrams exhibit many dynamic critical points, such as tricritical (•), zero-temperature critical (Z), triple (TP) and multicritical (A) points. According to values of Hamiltonian parameters, besides the paramagnetic (P), ferromagnetic (F) fundamental phases, one coexistence or mixed phase region, (F+P) and the reentrant behavior exist in the system. The results are in good agreement with some experimental and theoretical results.     

Magnetic and transport properties of Gd0.9A0.1CoO3−δ (A=Ba, Sr)

The X-ray diffraction, magnetization and electrical conductivity measurements for Gd_0.9A_0.1CoO_3−δ (A=Ba, Sr) have been made. The complicated magnetic behavior, including the paramagnetic-ferromagnetic-antiferromagnetic and paramagnetic-ferromagnetic transitions, was found for Ba- and Sr-doped samples. The gradual insulator-metal transitions were observed in a wide temperature range T=600−800 K. The complex magnetic and transport data could be explained on the basis of the structural phase separation.     

Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D(t,x)=D(t)|x|^−θ, subject to absorbing boundary condition and the conventional initial condition p(x,0)=δ(x−x₀). We obtain explicit analytical expressions for the probability distribution, the first passage time distribution, the mean first passage time and the mean squared displacement, and discuss their behavior corresponding to different time dependent diffusion coefficients.     

Oxygen nonstoichiometry, defect structure and electrical properties of LaFe0.7Ni0.3O3 − δ

Oxygen nonstoichiometry (δ), total conductivity (σ) and thermoelectric power (S) of the LaFe_0.7Ni_0.3O_3 − δ sample have been studied as functions of temperature and oxygen partial pressure. Based on the results of the direct reduction of the sample in hydrogen flow at 1100 °C the absolute oxygen content (3 − δ) has been found to vary from 2.999 to 2.974 in the range of 1273-1373 K and 10^− 3-0.21 atm. The point defect equilibrium models have been proposed and fitted to the set of experimental data in the form of log p(O₂) = f(δ)_T dependences. The values of standard thermodynamic quantities of defect formation reactions have been assessed. The joint analysis of oxygen nonstoichiometry, total conductivity and thermoelectric power has been performed using a small-polaron approach. The values of partial conductivity, partial thermopower and mobilities of electronic charge carriers have been calculated. The p-type semiconducting behavior of LaFe_0.7Ni_0.3O_3 − δ has been explained by the higher mobility values of electron holes than those of electrons in the whole range of thermodynamic parameters studied.     

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume-Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume-Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h₀/zJ) and (T/zJ, D/zJ), where T absolute temperature, h₀, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z).     

Phase behavior of unsymmetrical dimers on a square lattice

Monte Carlo simulations in the grand canonical ensemble have been carried out to study phase transitions in monolayers formed by heterogeneous dimers, composed of segments A and B, on a square lattice. The unsymmetrical segment-segment interactions are assumed (u_AA ≠ u_BB). The systems with u_AB = u_BB = −1 and different AA-interactions studied in our previous work [W. R?ysko, M. Borówko, Surf. Sci. 520 (2002) 151] are reconsidered. The structural phase transitions at high temperatures are investigated. It is shown that topology of a phase diagram depends on the energy u_AA. For repulsive AA-interactions a triple point is found and the system belongs to the universality class of a tricritical point. When u_AA < 0 the critical line of the order-disorder transition terminates at a critical end point and the system belongs to the universality class of the 2D Ising model.     

The effect of the B-site size on the structural,magnetic and electrical properties of La0.7Ca0.3MnO3−δ compounds

The perovskite-type ceramic La_0.7Ca_0.3MnO_3−δ was prepared by the solid-state reaction with 0.00?δ?0.15. X-ray diffraction, electrical and magnetic measurements were performed to examine the effect of the B-site size on the properties of these materials. We have found that the structure is orthorhombic for 0.00?δ?0.075 and becomes rhombohedral for 0.10?δ?0.15. The measurements of the magnetization as a function of the temperature, M(T), shows a ferromagnetic-paramagnetic transition at the Curie temperature T_C for δ=0.00. When increasing δ, these curves report the presence of two types of transitions. The first one is from the ferromagnetic to the antiferromagnetic state, indicating the existence of a charge-ordering state (T_CO). The second antiferromagnetic-paramagnetic transition occurs at the Neel temperature T_N. The temperature dependence of the resistivity ρ(T), indicates a metallic behaviour at low temperature (T<T_p) and a semiconductor behaviour at high temperature (T>T_p) for δ=0.00. For 0.05?δ?0.10, the ρ(T) curves shows a semiconductor behaviour revealing the disappearance of the metallic state which reappear at low temperature for δ=0.125 and 0.150.     

Defect structure and oxide ion transport in Sr- and Cr-doped LaCoO3 − δ

The results of oxygen nonstoichiometry, δ, measured by means of coulometric technique as a function of oxygen partial pressure, p_o2, in temperature range 1223 ≤ T, K ≤ 1323 are presented for the perovskite-type doped with chromium solely LaCo_0.7Cr_0.3O_3 − δ and simultaneously doped both with strontium and chromium La_0.7Sr_0.3Co_0.7Cr_0.3O_3 − δ cobaltites. The limit stability of the latter was found to exceed that of undoped cobaltite LaCoO_3 − δ on six orders of magnitude of p_o2 at a given temperature. The modeling of the defect structure of these perovskites was carried out and its adequate model was found. Chemical and self-diffusion coefficients of oxygen vacancies and oxygen ionic conductivity and ionic transport numbers were measured for the first time for La_0.7Sr_0.3Co_0.7Cr_0.3O_3 − δ as a function of oxygen partial pressure p_o2and temperature in the ranges − 4 ≤ log(p_o2, atm) ≤ 0 and 1223 ≤ T, K ≤ 1323, respectively. The additional substitution of Sr for La in LaCo_0.7Cr_0.3O_3 − δ was shown to lead to noticeable increase of ionic conductivity and oxygen chemical diffusion coefficient at given values of oxygen partial pressure and temperature as compared to lanthanum cobaltite doped with chromium solely. Self-diffusion coefficient of oxygen vacancies and their mobility in La_0.7Sr_0.3Co_0.7Cr_0.3O_3 − δ were found to be dependent on oxygen partial pressure and nonstoichiometry unlike undoped and doped with chromium lanthanum cobaltites.     

Phase diagram of the two-dimensional Ising model with random competing interactions

An Ising model with ferromagnetic nearest-neighbor interactions J₁ (J₁>0) and random next-nearest-neighbor interactions [+J₂ with probability p and −J₂ with probability (1−p); J₂>0] is studied within the framework of an effective-field theory based on the differential-operator technique. The order parameters are calculated, considering finite clusters with n=1,2, and 4 spins, using the standard approximation of neglecting correlations. A phase diagram is obtained in the plane temperature versus p, for the particular case J₁=J₂, showing both superantiferromagnetic (low p) and ferromagnetic (higher values of p) orderings at low temperatures.     

Perpendicular magnetic anisotropy and magnetic proximity effect in Pt1−δFeδ/Co multilayer films

The perpendicular magnetic anisotropy (PMA) and magnetization in Pt_1−δFe_δ/Co (δ=0, 0.017, 0.04 and 0.06) multilayer films have been investigated. It is found that, on adding a small amount of Fe into the Pt layers, Pt/Co multilayer films maintain well-defined PMA at both 5 and 300 K along with significantly enhanced magnetization even at room temperature, which is far greater than the Curie temperature of Pt_1−δFe_δ dilute alloys. Further study demonstrates that the large enhancement of the magnetization in the Fe doped Pt/Co multilayers at 300 K arises from the bulk moment of the Pt_1−δFe_δ layers at the interface region, where the ferromagnetic order persists up to room temperature due to the strengthened exchange interactions between Fe atoms via strongly polarized Pt near the Pt_1−δFe_δ/Co interfaces. For the Pt_0.96Fe_0.04/Pt multilayers, the magnetically ordered region in each Pt_0.96Fe_0.04 layer extends over at least 10 Å from the interface at room temperature.     

Oxygen deficiency, vacancy clustering and ionic transport in (La,Sr)CoO3 − δ

The equilibrium p(O₂)-T-δ diagrams of perovskite-type La_1 − xSr_xCoO_3 − δ (x = 0.3-0.7), collected at 873-1223 K in the oxygen partial pressure range 10^− 5-1 atm by coulometric titration and thermogravimetric analysis, were analyzed in order to appraise the effects of the point-defect interactions. The nonstoichiometry variations were adequately described combining the rigid-band approach for delocalized holes and the pair-cluster formation reaction involving oxygen vacancies and Co²⁺ cations, whilst coulombic repulsion between the positively charged vacancies can be neglected. The resultant relationships between the oxygen chemical potential and mobile vacancy concentration were used for numerical regression analysis of the steady-state oxygen permeation through dense La_1 − xSr_xCoO_3 − δ membranes, affected by the surface exchange kinetics when Sr²⁺ content is higher than 40-50%. The calculated ionic conductivity is strongly influenced by the defect association processes, and decreases with decreasing concentration of the mobile vacancies as clustering starts to prevail on reduction. The Mössbauer spectroscopy studies of La_1 − xSr_xCoO_3 − δ, doped with 1 mol% ⁵⁷Fe isotope and moderately reduced at p(O₂) ≈ 10⁻⁵ atm, show no long-range vacancy ordering at x ≤ 0.5.     

Finite-Size Scaling for the 2D Ising Model with Minus Boundary Conditions

We study the magnetization m _L (h, ) for the Ising model on a large but finite lattice square under the minus boundary conditions. Using known large-deviation results evaluating the balance between the competing effects of the minus boundary conditions and the external magnetic field h, we describe the details of its dependence on h as exemplified by the finite-size rounding of the infinite-volume magnetization discontinuity and its shift with respect to the infinite-volume transition point.     

Collision induced absorption spectra of the fundamental band of D2 in binary mixtures D2-Kr at 298 K

The enhancement spectrum of the collision induced absorption of D₂ in its fundamental band region 2600-4000 cm⁻¹ in binary mixtures D₂-Kr was studied at 298 K for base densities of D₂ in the range 9-20 amagat and for partial densities of Kr in the range 7-120 amagat. The binary absorption coefficient of the band has been determined from the measured integrated absorption coefficient and found to be 3.9 × 10⁻³ cm⁻² amagat⁻². An analysis of the experimental spectrum was carried out by assuming appropriate line-shape functions and the half-width parameters δ₁, δ₂, δ_d and δ_c of the long range quadrupole, and of the short range overlap induced transitions have been determined. Good agreement was obtained between the recorded spectrum of the fundamental band and the synthetic profile.     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.