Phase diagram for the <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) model with defects of “random local field” type and verity of the Imry–Ma theorem

It is shown that the Imry–Ma theorem stating that in space dimensions d < 4 the introduction of an arbitrarily small concentration of defects of the “random local field” type in a system with continuous symmetry of the n-component vector order parameter (O(n) model) leads to long-range order collapse and to the occurrence of a disordered state is not true if the anisotropic distribution of the defect-induced random local field directions in the space of the order parameter gives rise to the effective anisotropy of the “easy axis” type. In the case of a weakly anisotropic field distribution, in space dimensions 2 ≤ d < 4 there exists some critical defect concentration, above which the inhomogeneous Imry–Ma state can exist as an equilibrium one. At a lower defect concentration, long-range order takes place in the system. In the case of a strongly anisotropic field distribution, the Imry–Ma state is suppressed completely and long-range order state takes place at any defect concentration.     

Imry–Ma disordered state induced by impurities of “random local anisotropy” type in the system with <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) symmetry

For the system with the n-component order parameter (O(n)-model), conditions for initiation of the Imry–Ma disordered state resulting from the influence of impurities of the “random local anisotropy” type were discovered. The initiation of such a state was shown to be possible if the distribution of local anisotropy axes directions in the order parameter space is nearly isotropic, and the limiting degree of the distribution anisotropy was found. For a higher anisotropy in the distribution of local axes directions, the long-range order in the system holds true even in the presence of impurities of the given type.     

Anisotropic models of polymer ferroelectrics

The phase transitions to an ordered state in three-dimensional polymer systems that consist of flexible and rigid segments with intrachain and interchain orientational-deformational dipole interactions are considered. The statistic properties of the proposed models correspond to the Gaussian and spherical approximations that are used to describe the behavior of anisotropic Heisenberg ferroelectrics and ferromagnets. In the three-dimensional models under consideration, there exists a critical point T _c where a secondorder phase transition from an isotropic state to a state with long-range orientational order occurs. The laws of variation in the temperature T _c as a function of anisotropy of the interactions are established by analytical methods. The temperature dependences of the long-range dipole order parameter for a given chain bending are calculated and the results are compared with the experimental data obtained by the piezoelectric pressure step (PPS) method for thick ferroelectric PVDF and P(VDF-TrFE) polymer films.     

Finite size and surface effects on the magnetic properties of cobalt ferrite nanoparticles

Cobalt ferrite, CoFe₂O₄, nanoparticles in the size range 2–15 nm have been prepared using a non-aqueous solvothermal method. The magnetic studies indicate a superparamagnetic behavior, showing an increase in the blocking temperatures (ranging from 215 to more than 340 K) with the particle size, D _TEM. Fitting M versus H isotherms to the saturation approach law, the anisotropy constant, K, and the saturation magnetization, M _S, are obtained. For all the samples, it is observed that decreasing the temperature gives rise to an increase in both magnetic properties. These increases are enhanced at low temperatures (below ~160 K) and they are related to surface effects (disordered magnetic moments at the surface). The fit of the saturation magnetization to the T ² law gives larger values of the Bloch constant than expected for the bulk, increasing with decreasing the particle size (larger specific surface area). The saturation magnetization shows a linear dependence with the reciprocal particle size, 1/D _TEM, and a thickness of 3.7 to 5.1 Å was obtained for the non-magnetic or disordered layer at the surface using the dead layer theory. The hysteresis loops show a complex behavior at low temperatures (T ≤ 160 K), observing a large hysteresis at magnetic fields H > ~1000 Oe compared to smaller ones (H ≤ ~1000 Oe). From the temperature dependence of the ac magnetic susceptibility, it can be concluded that the nanoparticles are in magnetic interaction with large values of the interaction parameter T ₀, as deduced by assuming a Vogel–Fulcher dependence of the superparamagnetic relaxation time. Another evidence of the presence of magnetic interactions is the almost nearly constant value below certain temperatures, lower than the blocking temperature T _b, observed in the FC magnetization curves.     

Azimuthal anisotropy of the emission of fragments and relativistic particles in collisions between iron nuclei of momentum 2.5 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon and photoemulsion nuclei

The azimuthal anisotropy of the emission of fragments and relativistic particles in collisions between ⁵⁶Fe nuclei of momentum 2.5 GeV/c per nucleon and photoemulsion nuclei is measured. For semicentral collisions at impact-parameter values in the range 0.12 ≤ b/b_max ≤ 0.70, charged fragments and relativistic particles are predominantly emitted in the direction orthogonal to the nuclear-reaction plane. The azimuthal-asymmetry parameter P₂ for fragments whose charge numbers are Z = 1, 2 and Z ≥ 3 takes values of, respectively, ?0.192±0.057, ?0.28±0.07, and ?0.39±0.12. Evaporated b particles have an isotropic azimuthal distribution.     

A mechanism of long-range order induced by random fields: Effective anisotropy created by defects

A microscopic mechanism of the long-range order in two-dimensional space induced by random local fields of crystal defects has been found. The impurity-induced effective anisotropy has been shown to arise in the system due to anisotropic distribution of impurity-induced random local field directions in the n-dimensional space of vector order parameter with the O(n) symmetry. The expression for the effective anisotropy constant has been obtained. A weak anisotropy of the “easy axis” type transforms the X–Y model and the Heisenberg model to the class of Ising models, and brings into long-range order existence in the system.     

QCD sum rules for the coupling constants <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">KYN</Emphasis></Subscript> and <Emphasis Type="Italic">g</Emphasis><Subscript>KYΞ</Subscript>

New relations between Borel QCD sum rules for the strong couplings of baryons to kaons are derived. It is shown that, on the basis of the sum rules for the coupling constants g _πΣΣ and g _πΣΛ, the corresponding sum rules can be directly obtained for the coupling constants g _KYN and g _KYΞ, Y = Σ,Λ. The values of these coupling constants are calculated in the fiducial interval 1.0 ≤ M ² ≤ 1.4 GeV² at t = ?1.     

Reconstruction of the 2D hole gas spectrum for selectively doped <Emphasis Type="Italic">p</Emphasis>-Ge/Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>S<Subscript>ix</Subscript> heterostructures

The magnetic field (0≤B≤32 T) and temperature (0.1≤T≤15 K) dependences of longitudinal and Hall resistivities have been investigated for p-Ge_0.93Si_0.07/Ge multilayers with different Ge layer widths 12≤d _w ≤20 nm and hole densities p _s =(1–5)×10¹⁵ m^?2. An extremely high sensitivity of the experimental data (the structure of magnetoresistance traces, relative values of the inter-Landau-level gaps deduced from the activation magnetotransport, etc.) to the quantum well profile is revealed in the cases where the Fermi level reaches the second confinement subband. An unusually high density of localized states between the Landau levels is deduced from the data. Two models for the long-range random impurity potential (the model with randomly distributed charged centers located outside the conducting layer and the model of the system with a spacer) are used to evaluate the impurity potential fluctuation characteristics: the random potential amplitude, the nonlinear screening length in the vicinity of integer filling factors v=1 and v=2, and the background density of states (DOS). The described models are suitable for explanation of the observed DOS values, while the short-range impurity potential models fail. For half-integer filling factors, a linear temperature dependence of the effective quantum Hall effect plateau-plateau (PP) transition widths v₀(T) is observed, contrary to the expected scaling behavior of the systems with short-range disorder. The finite T→0 width of the PP transitions may be due to an effective low-temperature screening of a smooth random potential due to the Coulomb repulsion of electrons.     

Anisotropy induced by impurities of “random local field” type in <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) models and suppression of the Imry–Ma inhomogeneous state

It is shown that in a system with anisotropic distribution of the impurity-induced random local field directions in the n-dimensional space of a vector order parameter with the O(n) symmetry, the impurityinduced effective anisotropy arises for the space dimensionality 2 < d < 4. If the anisotropy constant exceeds the threshold value, then an inhomogeneous state predicted by Imry and Ma becomes energetically unfavorable, and the system goes back to a state with the long-range order.     

Schur Polynomials and The Yang-Baxter Equation

We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map \({g \mapsto R (g)}\) from \({ \rm{GL}(2, \mathbb{C}) \times \rm{GL}(1, \mathbb{C})}\) to End \({(V \otimes V)}\) , where V is a two-dimensional vector space such that if \({g, h \in G}\) then R ₁₂(g)R ₁₃(gh) R ₂₃(h) = R ₂₃(h) R ₁₃(gh)R ₁₂(g). Here R _{i j} denotes R applied to the i, j components of \({V \otimes V \otimes V}\) . The image of this map consists of matrices whose nonzero coefficients a ₁, a ₂, b ₁, b ₂, c ₁, c ₂ are the Boltzmann weights for the non-field-free six-vertex model, constrained to satisfy a ₁ a ₂ + b ₁ b ₂ ? c ₁ c ₂ = 0. This is the exact center of the disordered regime, and is contained within the free fermionic eight-vertex models of Fan and Wu. As an application, we show that with boundary conditions corresponding to integer partitions λ, the six-vertex model is exactly solvable and equal to a Schur polynomial s _λ times a deformation of the Weyl denominator. This generalizes and gives a new proof of results of Tokuyama and Hamel and King.     

Investigation of the <Emphasis Type="Italic">Hττ</Emphasis> and <Emphasis Type="Italic">Hbb</Emphasis> coupling constants for a scalar (pseudoscalar) Higgs boson at a future linear electron-positron collider

The possibility of setting constraints on the couplings of a scalar (pseudoscalar) Higgs boson to the tau lepton and the b quark in the reactions \(e^ + e^ - \to \nu \bar \nu \tau ^ + \tau ^ - \) and \(e^ + e^ - \to \nu \bar \nu b\bar b\) at a future linear electron-positron collider of total energy \(\sqrt s = 500 GeV\) is studied. The admixture of a new hypothetical pseudoscalar state of the Higgs boson in the H ff vertex is parametrized in the form (m _f /ν)(a+iγ₅b). On the basis of an analysis of differential distributions for the processes under study, it is shown that data from the future linear collider TESLA will make it possible to constrain the parameters a and b as ?0.32≤Δa≤0.24 and ?0.73≤b≤0.73 in the case of the reaction \(e^ + e^ - \to \nu \bar \nu \tau ^ + \tau ^ - \) and as ?0.026≤Δa≤0.027 and ?0.23≤b≤0.23 in the case of the reaction \(e^ + e^ - \to \nu \bar \nu b\bar b\). It is emphasized that the contribution of the fusion subprocess WW → H in the channel involving an electron neutrino is of particular importance, since this contribution enhances the sensitivity of data to the parameters being analyzed.     

Structural and magnetic phase transformations in the BiFeO<Subscript>3</Subscript>-CaFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> system

The crystal structure and magnetic properties of the Bi_{1 ? x} Ca _x Fe_{1 ? x/2}Nb _x/2O₃ system were studied. It is shown that, at x ≤ 0.15, the unit-cell symmetry of solid solutions is rhombohedral (space group R3c). Solid solutions with x ≥ 0.3 have an orthorhombic unit cell (space group Pbnm). The rhombohedral compositions are antiferromagnetic, while the orthorhombic compositions exhibit a small spontaneous magnetization due to Dzyaloshinski?-Moriya interaction. In CaFe_0.5Nb_0.5O₃, the Fe³⁺ and Nb⁵⁺ ions are partially ordered and the unit cell is monoclinic (space group P2₁/n). In the concentration range 0.15 < x < 0.30, a two-phase state (R3c + Pbnm) is revealed.     

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpiński gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with 0 ≤ J_b/J_a< 1, and an interesting crossover behavior between different phases at J_b/J_a = 1 is unveiled, whose dynamics can be described by the J_b/J_a-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpiński gasket are obtained in both the 1 / 3 plateau disordered phase and the 5/9 plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.     

A quantum-topological analysis of short (strong) H bonds in three-dimensional periodic crystals

The characteristics of the critical electron density points of the O-H···A fragment (A = O or N) in molecular crystals with short H bonds were analyzed in terms of the Bader quantum-topological theory of molecular structure. The wave functions (B3LYP/6-31G** approximation) of the ground state of 26 three-dimensional periodic crystals with experimentally determined structures were used. Intermediate-type interactions separating the limiting cases of covalent and closed shell-type interactions were found to be characterized by the following geometric parameters: 2.45 Å ≤ D(O···O) ≤ 2.6 Å, 1.35 Å ≤ d(H···O) ≤ 1.65 Å, and 1.0 Å ≤ d(O-H) ≤ 1.10 Å. Such interactions are observed in molecular crystals with the O-H···A fragment and high bridge proton mobility. Differences between H···O and H···N interactions were quantitatively characterized by the dependence of ρ _b on d(H···A), where A = O or N. The dependence parameter values were shown to be determined by the nature of the A atom that forms the H bond. The influence of the crystalline environment on systems with strong H bonds manifested itself by changes in the position of the bridge proton. The d(O-H)/d(H···O) ratio was, however, the same for gas-phase complexes and molecular crystals with weakly bent O-H···O fragments (∠O-H···O > 160°).     

Enhancement of superconductivity in disordered films by parallel magnetic field

We show that the superconducting transition temperature T _c (H) of a very thin highly disordered film with strong spin-orbital scattering can be increased by a parallel magnetic field H. This effect is due to the polarization of magnetic impurity spins, which reduces the full exchange scattering rate of electrons; the largest effect is predicted for spin-1/2 impurities. Moreover, for some range of magnetic impurity concentrations, the phenomenon of superconductivity induced by magnetic field is predicted: the superconducting transition temperature T _c (H) is found to be nonzero in the range of magnetic fields 0 < H* ≤ H ≤ H _c .     

Path integral approach for spaces of nonconstant curvature in three dimensions

In this contribution, I show that it is possible to construct three-dimensional spaces of nonconstant curvature, i.e., three-dimensional Darboux spaces. Two-dimensional Darboux spaces have been introduced by Kalnins et al., with a path integral approach by the present author. In comparison to two dimensions, in three dimensions it is necessary to add a curvature term in the Lagrangian in order that the quantum motion can be properly defined. Once this is done, it turns out that, in the two three-dimensional Darboux spaces which are discussed in this paper, the quantum motion is similar to the two-dimensional case. In D _3d-I, we find seven coordinate systems which separate the Schrödinger equation. For the second space, D _3d-II, all coordinate systems of flat three-dimensional Euclidean space which separate the Schrödinger equation also separate the Schrödinger equation in D _3d-II. I solve the path integral on D _3d-I in the (u, v, w) system and on D _3d-II in the (u, v, w) system and in spherical coordinates.     

Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O(3) symmetry) displays the inductor σ(ω) = (iωL)^?1 and capacitor iωC behaviors for the ordered and disordered phases, respectively. Both constants, C and L, have the same scaling dimension as that of the reciprocal paramagnetic gap Δ^?1. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O(2) case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap Δ directly. Thereby, the set of critical amplitude ratios as to C, L and Δ are estimated with the finite-size-scaling analysis for the cluster with N ≤ 34 spins.     

New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values \(\{a_{1},a_{2},a_{3},\ldots ,a_{N}\}\) and a function \(g:\textbf {R}\rightarrow \{0,1\}\), we shall determine the following values \(\{g(a_{1}),g(a_{2}),g(a_{3}),\ldots , g(a_{N})\}\) simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of \(N\). Next, we consider it as a number in binary representation; M₁ = (g(a₁),g(a₂),g(a₃),…,g(a _N )). By using \(M\) parallel quantum systems, we have \(M\) numbers in binary representation, simultaneously. The speed of obtaining the \(M\) numbers is shown to outperform the classical case by a factor of \(M\). Finally, we calculate the product; \( M_{1}\times M_{2}\times \cdots \times M_{M}. \) The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.     

Estimation of the Density of the Self-Interacting Dark-Matter Component within a Clump with Allowance for Recombination

The model of dark matter featuring a component in the form of free particles and antiparticles (a, ā ) possessing self-interaction of the Coulomb type is considered. Darkmattermay form small-scale clumps where the annihilation of particles a and ā is enhanced. This annihilation may lead to observable effects (in cosmic rays, for example) and/or to the destruction of these clumps. However, there is an ambiguity in describing the annihilation (via recombination) of very slow particles, which may include a and ā in clumps. The effect of annihilation (in terms of the residual number of free particles a and ā in clumps) is estimated within two approaches (simplified quantum-mechanical and classical) at chosen parameter values.     

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρ _s in the ordered phase and the vortex-condensate stiffness ρ _v in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρ _s,v /Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρ _s /ρ _v admits a quantitative measure of deviation from selfduality.