Temperature dependences of thermal expansion and exchange magnetostriction of holmium and dysprosium single crystals

Information on the character of the temperature relationships of linear expansion coefficients (α_a, α_c) and exchange magnetostrictions (λ_a, λ_a) of single crystal Ho and Dy, based on temperature dependence of thec- anda-axis lattice constants, were accurately determined by X-ray diffraction from 4,2 to 300 K. In the helical phases we observed a large anisotropy of expansion coefficients (α_a>0, α_c<0) and their variations at 24,5, 45 and 96 in Ho and 156 K in Dy. These anomalies were caused by the commensurate transitions. The Curie transition in Ho is found to be of the 1-st order.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Third-order elastic moduli of single-layer graphene

In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors μ, analytical expressions have been obtained for three third-order independent elastic constants c _ijk (μ, ζ) of single-layer graphene, where ζ = (2α − β)/(4α + β) is the Kleinman internal displacement parameter and α and β are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure p have been determined. It has been shown that the moduli c ₁₁ and c ₂₂ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.     

Phase Diagram of Ising Systems with Additional Long Range Forces

We consider ferromagnetic Ising systems where the interaction is given by the sum of a fixed reference potential and a Kac potential of intensity λ≥0 and scaling parameter γ>0$. In the Lebowitz Penrose limit γ→0⁺$ the phase diagram in the (T,λ) positive quadrant is described by a critical curve λ^mf(T), which separates the regions with one and two phases, respectively below and above the curve. We prove that if $λ>^mf(T), i.e. above the curve, there are at least two Gibbs states for small values of γ. If instead λ<λ^mf(T) and if the reference Gibbs state (i.e. without the Kac potential) satisfies a mixing condition at the temperature T, then, at the same temperature the full interaction (i.e. with also the Kac potential) satisfies the Dobrushin Shlosman uniqueness condition for small values of γ so that there is a unique Gibbs state. Received: 9 April 1996 / Accepted: 26 November 1996     

Superconducting triplet spin valve

We study the critical temperature T _c of SFF trilayers (S is a singlet superconductor, F is a ferromagnetic metal), where the long-range triplet superconducting component is generated at noncollinear magnetizations of the F layers. We demonstrate that T _c can be a nonmonotonic function of the angle α between the magnetizations of the two F layers. The minimum is achieved at an intermediate α, lying between the parallel (P, α = 0) and antiparallel (AP, α = π) cases. This implies a possibility of a “triplet” spin-valve effect: at temperatures above the minimum T _c ^Tr but below T _c ^P and T _c ^AP, the system is superconducting only in the vicinity of the collinear orientations. At certain parameters, we predict a reentrant T _c (α) behavior. At the same time, considering only the P and AP orientations, we find that both the “standard” (T _c ^P < T _c ^AP) and “inverse” (T _c ^P > T _c ^AP) switching effects are possible depending on parameters of the system.     

Superconducting state parameters of CuCZr100-C metallic glasses

The theoretical investigation of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _c, isotope effect exponent α and effective interaction strength N ₀ V of ten Cu _C Zr_100−C metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Three local field correction functions proposed by Hartree (H), Taylor (T) and Ichimaru-Utsumi (IU) are used in the current investigation to study the screening influence on the aforesaid properties. It is observed that the electron-phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ*, isotope effect exponent α and effective interaction strength N ₀ V show weak dependences on local field correction functions. The T _c obtained from IU-local field correction function are found an excellent agreement with available theoretical or experimental data. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in metallic glasses.      

Magnetostriction of the spin-Peierls compound CuGeO3

The longitudinal and transverse magnetostriction λ of the spin-Peierls compound CuGeO₃ in the b-c plane is measured in magnetic fields up to 20 T both above and below the transition temperature T _sp=14.3K. It is found that for a given crystallographic direction the value of magnetostriction is weakly dependent on the magnetic field direction. In the uniform U phase at T⩾T _sp, λ is negative and approximately equal in the b and c directions, while in the dimerized D phase at T<T _sp, λ is positive and λ _b >λ _c . At low temperatures, λ increases sharply at the magnetic-field-induced transition from the dimerized to the magnetic M phase. The experimental data allow estimation of the stress derivatives of the antiferromagnetic intrachain exchange interaction parameter and of the stress dependence of the critical field of the D-Mphase transition. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 156–159 (10 August 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Extended modes and energy dynamics in two-dimensional lattices with correlated disorder

We study the nature of the vibrational modes in a two-dimensional harmonic lattice with long-range correlated random masses, with power-law spectral density S(k)∼1/k^α. We obtain numerically the scale invariance of the fluctuations of the relative participation number and the local density of states. We find signatures of extended vibrational modes when α>α_c and α_c depends on the magnitude of disorder. In order to confirm this claim, we also study the time evolution of an initially localized perturbation of the lattice. We show that the second moment of the spatial distribution of the energy displays a ballistic regime when α>α_c, in agreement with the occurrence of extended vibrational modes.     

On the investigation of magnetic critical phenomena in ferromagnets by μSR and PAC

On the basis of current theoretical views on the critical phenomena in isotropic Heisenberg ferromagnets the power temperature behavior Λ=c(τ)λ₀τ^-w has been derived for the muon spin relaxation rate Λ as π-T _c ⁻¹ (T-T _c ) → 0⁺. It is shown that the crossover from an exchange critical regime to a dipolar one is accompanied not only with the change in the critical exponentw in the above law, but also with the reduction of the coefficientc(π). A comparison with the temperature behaviour of the inverse nuclear relaxation timet _R ⁻¹ measured in the PAC experiment is carried out.     

Harmonically trapped ideal quantum gases

We solve the problem of a Bose or Fermi gas in d-dimensions trapped by δ ⩽ d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature T _c if and only if d + δ > 2, along with a jump in the specific heat at T _c if and only if d + δ > 4. Specific heats for both gas types precisely coincide as functions of temperature when d + δ = 2. The trapped system behaves like an ideal free quantum gas in d + δ dimensions. For δ = 0 we recover all known thermodynamic properties of ideal quantum gases in d dimensions, while in 3D for δ = 1, 2 and 3 one simulates behavior reminiscent of quantum wells, wires anddots, respectively. Good agreement is found between experimental critical temperatures for the trapped boson gases ₃₇ ⁸⁷Rb, ₃ ⁷Li, ₃₇ ⁸⁵Rb, ₂ ⁴He, ₁₉ ⁴¹K and the known theoretical expression which is a special case for d = δ = 3, but only moderate agreement for ₁₁ ²⁷Na and ₁ ¹H. Received 17 July 2002 / Received in final form 14 October 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: mdgg@hp.fciencias.unam.mx     

Investigation of impurity effects in La2?xSrxCu1?yMyO4 (M=Ga,Zn) by electronic specific heat

The electronic specific heat C_el was studied at T≤10K on Ga- and Zn-doped La_2−xSr_xCuO₄ (0.16≤x≤0.22). In pure La_2−xSr_xCuO₄ (0.16≤x≤0.22), the C_el at T<T_c contains only a T² component but no T-linear one, which is peculiar to a clean d-wave superconductor. Partial substitution of Ga or Zn for Cu changes the T²-term of C_el into a quite different one described by the sum of a T-linear and a nearly T³ term. The coefficient of the T-linear term, γ, markedly increases with Zn-or Ga-content. The λ/λ_N vs. T_c/T_co relation for Zn-doped samples with x≥0.2 is in good agreement with the theoretical curve for resonant impurity scattering in a d-wave superconductor, while those for Ga-doped samples and for Zn-doped samples with x<0.2 deviate slightly from the theoretical curve. Such a deviation will be discussed in relation to the change in the magnetic properties of the present system caused by impurity-doping.     

Criticality of the mean-field spin-boson model: boson state truncation and its scaling analysis

The spin-boson model has nontrivial quantum phase transitions at zero temperature induced by the spin-boson coupling. The bosonic numerical renormalization group (BNRG) study of the critical exponents β and δ of this model is hampered by the effects of boson Hilbert space truncation. Here we analyze the mean-field spin boson model to figure out the scaling behavior of magnetization under the cutoff of boson states N _b . We find that the truncation is a strong relevant operator with respect to the Gaussian fixed point in 0 < s < 1/2 and incurs the deviation of the exponents from the classical values. The magnetization at zero bias near the critical point is described by a generalized homogeneous function (GHF) of two variables τ = α – α _c and x = 1/N _b . The universal function has a double-power form and the powers are obtained analytically as well as numerically. Similarly, m(α = α _c ) is found to be a GHF of ϵ and x. In the regime s > 1/2, the truncation produces no effect. Implications of these findings to the BNRG study are discussed.     

Finite-size scaling in systems with long-range interaction

The finite-size critical properties of the (n) vector ϕ⁴ model, with long-range interaction decaying algebraically with the interparticle distance r like r ^{-d - σ}, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature T _c. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. 0 < σ < 2 and it turns out to be exponential in case of short-range interaction i.e.σ = 2. The results are valid for arbitrary dimension d, between the lower ( d _< = σ) and the upper ( d _> = 2σ) critical dimensions. Received 2 July 2001 and Received in final form 4 Septembre 2001     

Chain orientation in natural rubber, Part II: 2H-NMR study

Stress-induced crystallisation (SIC) and stress-induced melting (SIM) in natural rubbers (NR), unfilled and filled with carbon black (CB) have been studied by ²H-NMR measurements. Various materials have been swollen with small amount (< 2%) of deuterated alkane chains. The orientation of the amorphous chains, then the local deformation of the amorphous chains during deformation cycles and during stress relaxation, permits to clarify the SIC and SIM processes during hardening and recovery. By mechanical, WAXS and NMR measurements one determines the same critical draw ratio for appearance λ_A and disappearance λ_E of the crystallites. It is demonstrated that the hysteresis observed by the different techniques (stress σ, crystallinity χ, NMR splitting Δν) are due to the supercooling effect ( λ_A > λ_E, at constant temperature). During hardening at constant strain rate it is found that the local draw ratio remains constant and equal to λ_A, whereas the crystallinity increases linearly with the macroscopic draw ratio λ. The hardening σ ∼ (λ - λ_A)² is then interpreted as a reinforcement effect due to the crystallites, which act as new crosslinks. This confirms the prediction of Flory. In filled rubber the same effects are observed, and the stress amplification factor is determined as a function of the CB content. It is found that the fillers act as nucleation centres for the NR crystallites. The reinforcement of such materials is due principally to this nucleation effect and to the presence of a super network formed by both the NR crystallites and the CB fillers.     

Effects of size and surface anisotropy on thermal magnetization and hysteresis in the magnetic clusters

Based on Monte Carlo simulation, the spin configurations, thermal magnetization and hysteresis loops of the clusters coated by the surface shell with radial anisotropy are studied. Interestingly, a new multidomain containing a few of subdomains whose easy directions are along those of the configurational anisotropy, a magnetization curve in steps and a first order phase transition from the single domain to the multidomain in the thermal and field magnetization processes, are found, which is as a result of the interplay of the configurational anisotropy, the size effect, the surface anisotropy, the applied field and the thermal fluctuation. In this first order transition, we find a critical temperature, a critical surface anisotropy and a critical size. The simulated temperature dependence of the coercivity of the cluster with the surface anisotropy can be fitted by H_c (T)=H_c (0)(1-C_αT^α) with low value of α, which explains well the experimental results of the nanoparticles. Moreover, it is found that the hysteresis loops and coercivity are strongly affected by the cluster size and the thickness of the surface layer.     

A simple theory of condensation

A simple assumption of the emergence in gas of small atomic clusters consisting of c particles each leads to a phase separation (first-order transition). It reveals itself by the emergence of a “forbidden” density range starting at a certain temperature. Defining this latter value as the critical temperature predicts the existence of an interval with the anomalous heat capacity behavior c _p ∝ ΔT ^−1/c . The value c = 13 suggested in the literature yields the heat capacity exponent α = 0.077.     

A search for colour van der Waals interaction

It is suggested that the strength of nuclear colour van der Waals interaction, if present, can be determined by measuring deviations from Rutherford scattering of charged hadrons from nuclei, at energies well below the Coulomb barrier. Experimental limit on the strength of such a potential is obtained asλ<50, when the colour van der Waals potential is given byV(r)=λ(hc/r ₀)(r ₀/r)⁷, withr ₀, the scaling length, taken as 1 fm. This limit is obtained from an analysis of existing experiments and by performing scattering experiments of 3–4.6 MeV protons from a²⁰⁸Pb target.     

The Scaling Limit Geometry of Near-Critical 2D Percolation

We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for p = p _c+λδ^1/ν, with ν = 4/3, as the lattice spacing δ → 0. Our proposed framework extends previous analyses for p = p _c, based on SLE ₆. It combines the continuum nonsimple loop process describing the full scaling limit at criticality with a Poissonian process for marking double (touching) points of that (critical) loop process. The double points are exactly the continuum limits of “macroscopically pivotal” lattice sites and the marked ones are those that actually change state as λ varies. This structure is rich enough to yield a one-parameter family of near-critical loop processes and their associated connectivity probabilities as well as related processes describing, e.g., the scaling limit of 2D minimal spanning trees.