The potts glass in uniform and random fields: a monte carlo investigation

As a simple model of an anisotropic orientational glass with short range forces, the 3-state Potts model on the simple cubic lattice with nearest neighbor interactions drawn from a Gaussian distribution is considered. With Monte Carlo methods we study the response of the system to a uniform “field” which favors one of the states. This is motivated by experiments which apply stress that favors one molecular orientation of the quadrupolar glass. The responsem to that fieldh=H/k _BT is analyzed in terms of an expansionm= χ₁ h+χ₁ h ²+χ₁ h ³+..., where χ₁ is the linear susceptibility, and χ₂,χ₁₃ are nonlinear susceptibilities. Unlike the case of spin glasses, where the spin inversion symmetry of the system in the absence of fields implies χ₂≡0,χ₂ is nonzero here and diverges to ?∞ at the zero temperature transition of the model, while χ₃ diverges to +∞ as in spin glasses. At inifinite temperature, however, χ₁=1/3, χ₂=1/18 and χ₃=-1/54, i.e. the nonlinear susceptibilities have a different sign as at low temperature. In contrast, a random field does not induce a uniform order parameterm but only a glass order parameterq. The temperature dependence of this glass order parameterq(T) shows for intermediate field strength order parameterq(T) shows for intermediate field strength a maximum of the slopedq(T)/dT very similar to corresponding experiments.     

Monte Carlo test of the Goldstone mode singularity in 3D XY model

Monte Carlo simulations of magnetization and susceptibility in the 3D XY model are performed for system sizes up to L=384 (significantly exceeding the largest size L=160 considered in work published previously), and fields h ≥ 0.0003125 at two different coupling constants β=0.5, and β=0.55 in the ordered phase. We examine the prediction of the standard theory that the longitudinal susceptibility χ_∥ has a Goldstone mode singularity such that χ_∥ ∝h^-1/2 holds when h↦0. Most of our results, however, support another theoretical prediction that the singularity is of a more general form χ_∥ ∝h^ρ-1, where 1/2<ρ<1 is a universal exponent related to the ∼h^ρ variation of the magnetization.     

Electronic properties of arrayed K clusters in zeolite LTA with Si/Al = 1.5

Arrayed cationic K clusters including one 4s-electron in each cluster, i.e., K_m+1 ^m+, were incorporated into α-cages of zeolite LTA with Si/Al=1.5. Although no magnetic phase transition was observed regarding the temperature (T) dependence of magnetic susceptibilities originating from the 4s-electron spins (χ_spin) between 2 and 300 K, the χ_spin-T curve could be fitted by the sum of magnetic susceptibilities based on the Curie-Weiss law and Pauli paramagnetism. A possible explanation of this behavior is the existence of a narrow energy band formed out of 1s-cluster orbitals of arrayed K clusters, and the existence of a finite density of state at the Fermi energy.     

Strong dynamic magnetoelectric coupling in metamaterial

Magnetoelectric susceptibility (ξ) of classical magnetoelectrics is always substantially smaller that the geometric average of the electric (χ _e ) and magnetic (χ _m ) susceptibilities. Materials reaching the equality ξ ² = χ _e χ _m as a limiting value may thus be considered as ideal magnetoelectrics. Here we investigate the magnetoelectric susceptibility of a metamaterial built from split ring resonators both experimentally and within an equivalent circuit model. Due to a direct proportionality between electric polarization and magnetization, the magnetoelectric susceptibility of this metamaterial fulfils the equality ξ ² = χ _e χ _m at least in the dynamic regime.     

Spin state and exchange in the quasi-one-dimensional antiferromagnet KFeS2

We report the optical spectra and single crystal magnetic susceptibility of the one-dimensional antiferromagnet KFeS₂. Measurements have been carried out to ascertain the spin state of Fe³⁺ and the nature of the magnetic interactions in this compound. The optical spectra and magnetic susceptibility could be consistently interpreted using aS=1/2 spin ground state for the Fe³⁺ ion. The features in the optical spectra have been assigned to transitions within thed-electron manifold of the Fe³⁺ ion, and analysed in the strong field limit of the ligand field theory. The high temperature isotropic magnetic susceptibility is typical of a low-dimensional system and exhibits a broad maximum at ∼565K. The susceptibility shows a well defined transition to a three dimensionally ordered antiferromagnetic state atT _N=250 K. The intra and interchain exchange constants,J andJ′, have been evaluated from the experimental susceptibilities using the relationship between these quantities, andχ _max,T _max, andT _N for a spin 1/2 one-dimensional chain. The values areJ=−440.71 K, andJ′=53.94 K. Using these values ofJ andJ′, the susceptibility of a spin 1/2 Heisenberg chain was calculated. A non-interacting spin wave model was used belowT _N. The susceptibility in the paramagnetic region was calculated from the theoretical curves for an infiniteS=1/2 chain. The calculated susceptibility compares well with the experimental data of KFeS₂. Further support for a one-dimensional spin 1/2 model comes from the fact that the calculated perpendicular susceptibility at 0K (2.75×10⁻⁴ emu/mol) evaluated considering the zero point reduction in magnetization from spin wave theory is close to the projected value (2.7×10⁻⁴ emu/mol) obtained from the experimental data.     

Numerical and experimental investigations on the mach 2 pseudo-shock wave in a square duct

This paper describes numerical and experimental investigations for the multiple shock wave/turbulent boundary layer interaction in a Mach 2 supersonic square duct. The numerical simulation is carried out with the Harten-Yee second-order accuracy TVD scheme and the Baldwin-Lomax turbulence model. The flow conditions are a free-stream Mach number ofM _∞≈=2.0 and a Reynolds number ofRe _∞;=2.5×10⁷ and the flow confinements are δ_∞/h=0.15 (case A) and δ_∞/h=0.25 (case B), respectively. The computational results for both cases show good agreement with the experimental results. Based on these agreements, the flow quantities, which are very difficult to obtain experimentally, are analyzed by numerical simulation. Moreover, the effect of flow confinement on the pseudo-shock wave characteristics is also presented.     

Multiglass order and magnetoelectricity in Mn<Superscript>2+</Superscript> doped incipient ferroelectrics

“Multiglass” materials with simultaneous occurrence of two different glassy states extend the frame of conventional multiferroicity, which is devoted to crystalline materials with coexisting uniform long-range electric and magnetic ordering. The concept applies to Sr_0.98Mn_0.02TiO₃ ceramics, where A-site substituted Mn²⁺ ions are at the origin of both a polar and a spin cluster glass. Spin freezing is initiated below the dipolar glass temperature, T_g ^e ≈ 38 K, which is seemingly indicated by a divergence of the nonlinear susceptibility, χ₃. Below T_g ^m ≈ 34 K both glass phases are independently verified by memory and rejuvenation effects. Biquadratic interaction of the Mn²⁺ spins with ferroelectric correlations of their off-center pseudospins in the incipient ferroelectric host crystal SrTiO₃ explains the high spin glass temperature and comparably strong third-order magnetoelectric coupling between the polar and the magnetic degrees of freedom. Preliminary results on the related compound K_0.97Mn_0.03TaO₃ favorably comply with the magnetoelectric multiglass concept.     

Quasi-long-range order in the random anisotropy Heisenberg model

The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r ₁)m(r ₂)〉∼|r ₁−r ₂|^{− 0.62ε}. The magnetic susceptibility diverges at low fields as χ∼H ^−1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Die Magnetische SuszeptibilitÄt von Kristallinem n-CdGeAs2

The specific magnetic susceptibility of polycrystalline and powdered samples was measured between 77 °K and 570 °K. This dependence was interpreted in intrinsic range suggesting the susceptibility is given as a sum of contributions of the lattice ^G and of free carriers _L. The temperature dependence of the lattice susceptibility _G= _G ⁰ +T was checked: _G ⁰ =–2·35× ×10^–7, =4·5×10^–11. The contribution _L enabled to check the effective mass of holes m_h=0·25m₀ suggesting m_em_h.

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Herrn A. Hrubý gilt mein Dank für die Vorbereitung des polykristallinen Ingots von CdGeAs₂.     

Spin-dependent correction to the relativistic-electron mass in QED in the presence of an external electric field

A new expression is found for the spin-dependent contribution Δm _s to the self-energy of an electron moving with a transverse momentum p⊥ in an electric field. The structure of an asymptotic expansion of Δm _s (r, χ) as a function of two dynamical invariants r = γ _⊥⁻² and χ = γ _⊥|ɛ|/ɛ _c (γ _⊥² ≡ 1 + p _⊥²/m ² c ² and ɛ _c ≡ m ² c ³/|e|ℏ) is clarified with the aid of this expression. The expansion of Δm _s (r, χ) can be represented in the form of a Taylor series in r, the coefficients in this series, F ₀(χ), F ₁(χ), etc., being integrals of the Mellin type. The major coefficient F ₀(χ) is universal and, in the case of an appropriate interpretation of χ, describes well-known spin-dependent corrections to the mass in three different cases of a constant external field (for r → 0). The asymptotic properties of the function F ₁(χ) are studied in detail, but only order-of-magnitude estimates are obtained for F ₂(χ) and F ₃(χ). A comparison of these contributions revealed that, in the semiclassical region χ ≪ 1, r is indeed the parameter of the aforementioned expansion, while, for χ ≫ 1, the true parameter is rχ ² ≡ β ². In particular, the anomalous magnetic moment develops, owing to F ₁(χ), a term that grows logarithmically for χ ≫ 1, but which does not violate the hierarchy of terms in the Taylor series being considered, provided that β remains smaller than unity.     

(GL(<Emphasis Type="Italic">n</Emphasis> + 1, ℝ), GL(<Emphasis Type="Italic">n</Emphasis>, ℝ)) is a generalized Gelfand pair

Denote by G = GL(n + 1, ℝ) the group of invertible (n + 1) × (n + 1) matrices with real entries, acting on ℝ ⁿ⁺¹ in the usual way, and let H ₁ = GL(n, ℝ) be the stabilizer of the first unit vector e ₀. Let H ₀ = GL(1, ℝ) and set H = H ₀ × H ₁. It is known that the pair (G,H) is a generalized Gelfand pair. Define a character χ of H by χ(h) = χ(h ₀ h ₁) = χ0(h ₀) where χ0 is a unitary character of H ₀ (h ₀ ∈ H ₀, h ₁ ∈ H ₁). Let σ be the anti-involution on G given by σ(g) = ^t g. In this note, we show that any distribution T on G satisfying T(h ₁ gh ₂) = χ(h ₁ h ₂) T(g) (g ∈ G; h ₁, h ₂ ∈ H) is invariant under the anti-involution σ. This result implies that (G,H ₁) is a generalized Gelfand pair.     

deSitter space-time and rotation

A metric containing a parameterb is presented. It represents two distinct families of space-times, the Taub-nut family and the deSitter family, according asb=1 andb=4 respectively. The metric of the deSitter family of space-times contains a further parameterm. Whenm=0, the space-time is the usual homogeneous and isotropic deSitter space-time. But ifm≠0, the metric represents a space-time which is homogeneous but not isotropic satisfyingR _ik =Λg _ik . In this space-time, the 4-velocity of an observer at rest will have non-zero twist. The metric withb=4,m≠0 is interpreted as a metric representing a “rotating deSitter space-time”.     

Quantum Fisher Information in Two-Qubit Pure States

In terms of quantum Fisher information (QFI), a quantity χ ² was introduced by Pezzé and Smerzi (Phys. Rev. Lett. 102 100401, 2009). They pointed out that the inequality χ ²<1 was a sufficient condition for multiparticle entanglement. For the two-qubit symmetric states, we found that the inequality χ ²<1 is a necessary and sufficient condition for entanglement and spin squeezing, and that χ ² is equal to the second kind of spin squeezing parameter x₂²\xi _{2}^{2}. For the two-qubit asymmetric states, it is only a sufficient condition. In order to make it a necessary and sufficient condition, we extend the concept of the QFI and χ ², and generalize the relations among the entanglement measurement, the spin squeezing parameters and χ ² in symmetric pure states to arbitrary pure states.     

Quantum XY spin glass model with planar Dzyaloshinskii-Moriya interactions in longitudinal field

In the replica symmetric approximation and static limit in Matsubara “imaginary time”, the quantum XY spin glass model with planar Dzyaloshinskii-Moriya interaction in longitudinal field is investigated. Several thermodynamic quantities are calculated numerically as well as spin self-interaction and spin glass order parameter for spin S=1/2. It is shown that the entropy is not independent of the field. A crossover behavior of the specific heat depending on temperature is found. There is a deviation from the parabolic approximation, C/T=A+Bh ² . Received 11 March 1998     

A μSR Study of Er Spin Dynamics in (Y1−x Er x )Ni2B2C Superconductors

Zero field μSR has been used to probe rare earth spin dynamics in the magnetic superconductors, Y_1−x Er _x Ni₂B₂C. The muon spin relaxation function is stretched exponential, exp (−(λt)^β), in form, as usually found for spin glass systems above the glass temperature. However, the Y_1−x Er _x Ni₂B₂C compounds show no evidence of coexisting superconducting and static spin glass ground states even at concentrations below the critical value (x=0.6) for long range antiferromagnetic order. The temperature dependence of both the muon spin relaxation rate λ and the exponent β suggests that Er spin dynamics change significantly at the superconducting transition temperature. This revised version was published online in September 2006 with corrections to the Cover Date.     

The 2<Superscript>1/3</Superscript> rule for magnetic susceptibility of gadolinium

The dependences of the magnetization M and the magnetic susceptibility χ = ∂M/∂H of pure gadolinium (the concentration of foreign impurities is lower than 0.1 wt %) on the temperature T and the magnetic field H have been measured using a Quantum Design MPMS-5XL SQUID magnetometer. In this material, inhomogeneities of the atomic structure should not lead to a nonuniform distribution of the magnetic characteristics (including the Curie temperature T _C) over the volume of the sample. The obtained dependences of M and χ have been used to investigate the possibility of suppressing magnetic inhomogeneities of other types by magnetic fields with a strength of up to 50 kOe. It has been assumed that these inhomogeneities are suppressed when the specific relationship, namely, the 2^1/3 rule is fulfilled. The rule relates the portions of the dependence χ(T, H) which at the temperature T = T _C and at the maximum in the curve χ(T) (T = T _m ) depend on H in accordance with the H ^2/3 law. It has been shown that the portions separated from the experimental curves χ(T _C, H) and χ(T _m , H) obey the 2^1/3 rule.     

Kraus Operator-Sum Representation and Time Evolution of Distribution Functions in Phase-Sensitive Reservoirs

Using the thermal entangled state representation 〈η|, we examine the master equation (ME) describing phase-sensitive reservoirs. We present the analytical expression of solution to the ME, i.e., the Kraus operator-sum representation of density operator ρ is given, and its normalization is also proved by using the IWOP technique. Further, by converting the characteristic function χ(λ) into an overlap between two “pure states” in enlarged Fock space, i.e., χ(λ)=〈η _=−λ |ρ|η ₌₀〉, we consider time evolution of distribution functions, such as Wigner, Q- and P-function. As applications, the photon-count distribution and the evolution of Wigner function of photon-added coherent state are examined in phase-sensitive reservoirs. It is shown that the Wigner function has a negative value when kt\leqslant\frac 12ln( 1+m_￥) \kappa t\leqslant\frac {1}{2}\ln ( 1+\mu_{\infty}) is satisfied, where μ _∞ depends on the squeezing parameter |M|² of environment, and increases as the increase of |M|.     

The phase diagram of (NH4I)x(KI)1−x

The χ,T phase diagram of (NH₄I)_x(KI)_1−x has been determined using neutron diffraction experiments and dielectric spectroscopy. At low temperatures and with decreasing χ, the sequence γ, β, ε and glass phase has been detected. The critical concentration χ_c≈0.55 separates the glassy phase with frozen-in orientational disorder from the ε phase which reveals long-range orientational order. Close to χ_c our experiments reveal evidence for two subsequent glass transitions.