The Susceptibility of the Square Lattice Ising Model: New Developments

We have made substantial advances in elucidating the properties of the susceptibility of the square lattice Ising model. We discuss its analyticity properties, certain closed form expressions for subsets of the coefficients, and give an algorithm of complexity O(N⁶) to determine its first N coefficients. As a result, we have generated and analyzed series with more than 300 terms in both the high- and low-temperature regime. We quantify the effect of irrelevant variables to the scaling-amplitude functions. In particular, we find and quantify the breakdown of simple scaling, in the absence of irrelevant scaling fields, arising first at order |T–T_c|^9/4, though high-low temperature symmetry is still preserved. At terms of order |T–T_c|^17/4 and beyond, this symmetry is no longer present. The short-distance terms are shown to have the form (T–T_c)^p (log |T–T_c|)^q with pq². Conjectured exact expressions for some correlation functions and series coefficients in terms of elliptic theta functions also foreshadow future developments.     

On the local structure of the phase separation line in the two-dimensional Ising system

We investigate the structure of the phase separation line between the pure phases in the two-dimensional Ising model, the liquid and vapor phase in lattice gas language, at low temperatures. The fluctuations in the location of this line are known to diverge in the thermodynamic limit, something which is also believed to happen to the continuum liquid-vapor interface in three dimensions (in the absence of the gravitational field). We show that despite this global divergence it is possible to define precisely the local structure of the phase separation line. This has a finite, exponentially small, width at low temperatures which is related by a central limit theorem⁽¹⁾ to the width of the global fluctuations on the appropriate (divergent) length scale. The latter has been computed explicitly⁽²⁾ for all temperatures below the critical temperatureT _c, where it diverges as (T _c –T)^–1/2. We also prove a Gibbs formula for the surface tension at low temperature, which relates it to the local structure of the phase separation line.Supported in part by NSF grant No. M^rPHY 78-15920 and MCS78-01885.On leave from: Departement de Physique Théorique, Université de Louvain, Belgium.     

Annealing effect on the superconductivity of In2O3–ZnO thin films

We have investigated the relation among ρ–T characteristics, superconductivity, annealing conditions and the crystallinity of polycrystalline (In₂O₃)_1−x–(ZnO)_x films. We annealed as-grown amorphous films in air by changing annealing temperature and time. It is found that the films annealed at 200 °C or 300 °C for a time over 0.5 h shows the superconductivity. Transition temperature T_c and the carrier density n are T_c < 3.3 K and n ≈ 10²⁵–10²⁶ m⁻³, respectively. Investigations for films with x = 0.01 annealed at 200 °C have revealed that the T_c, n and crystallinity depend systematically on annealing time. Further, we consider that there is a suitable annealing time for sharp resistive transition because the transition width becomes wider with longer annealing times. We studied the upper critical magnetic field H_c2(T) for the film with different annealing time. From the slope of dH_c2/dT for all films, we have obtained the resistivity ρ dependence of the coherence length ξ(0) at T = 0 K.     

The ferroelectric phase transition in LiTaO3 studied by neutron scattering I. The Long-Range Order

Elastic neutron scattering from two reflections has been studied versus temperature, and the temperature dependence of the ferroelectric polarizationP(T) has been deduced. Neart _c =601°C the dependence is found to be classical: (T _c –T)^1/2. The study supports a model where the ferroelectric transition is accompanied by an order-disorder transition of the lithium ions.     

Low temperature1H NMR study of electronic structure parameters (T 1e T) in zirconium dihydride

Measurements of the proton-spin-lattice relaxation times (T ₁) are reported for zirconium dihydrides: ZrH_1.87, ZrH_1.93 and ZrH_2.00 at nominal frequency of 41 MHz, with emphasis on the low temperature (4.2–25 K) behaviour of theT ₁. The dominant contributions are originated from the hyperfine interactions of the protons with the conduction electrons and the paramagnetic impurities. The (T _1e T)^–1/2 values determined from the low temperature range (4.2–25 K) agree with those obtained in the extended range (4.2–300 K) as well as with the values reported by the other researches. The paramagnetic impurity contribution is found to be small and teperature independent.     

Structures and phase transition in Rb2NaHoF6

The phase transition at T_c=172(2) K and high as well as the low temperature structures at 205 K and 17 K were studied with a low temperature Guinier diffractometer and camera. A second order phase transition (Γ-condensation of the T_1g mode) lowers the symmetry from Fm3m at T>;T_c to I4/m at T<T_c. In the low temperature phase the octahedra are tilted (5.2 degrees at 17 K) and slightly stretched. The increase of the tilt angle and the linear increase of the tetragonal distortion suggests a mean field power law. This classical behaviour would agree with the assumption of a Jahn Teller splitting of the Ho³⁺ electronic state.     

Electrical conductivity improvement of strontium titanate doped lead vanadate glasses by nanocrystallization

The structural and electrical conductivity (σ) of annealed SrTiO₃–PbO₂–V₂O₅ glasses were studied. The annealing of initially glass samples leads to formation of nanocrystalline grains embedded in the glassy matrix. XRD patterns of the glass–ceramic samples show that nanocrystals were embedded in the glassy matrix with an average grain size of 32 nm. The glass–ceramic nanocrystals obtained by annealing at temperatures close to the crystallization temperature T_c exhibit enhancement of electrical conductivity up to four orders of magnitude than initially glasses. The enhancement of the electrical conductivity due to annealing was attributed to two interdependent factors: (i) an increase of concentration of V⁴⁺–V⁵⁺ pairs; and (ii) formation of defective, well-conducting regions along the glass–crystallites interfaces. From the conductivity temperature relation, it was found that small polaron hopping model was applicable at temperature above θ_D/2 (θ_D, the Debye temperature). The electrical conduction at T >θ_D/2 was due to non-adiabatic small polaron hopping (SPH) of electrons between vanadium ions. The parameters obtained from the fits of the experimental data to this model appear reasonable and are consistent with glass composition.     

Cu nuclear spin-spin relaxation in YBa2Cu3O6.98 and YBa2Cu4O8

We have measured the temperature (T) dependence of the transverse relaxation rate (T _G ^–1 ) of the Cu(1) nuclear spin in YBa₂Cu₃O_6.98 (T _c=92 K) and YBa₂Cu₄O₈ (T _c=82 K). From the scaling ratio ofT _G ^–2 (Cu1) toT _G ^–2 (Cu2), we have estimated the strength of a covalent bonding between the CuO₂ plane and the CuO chain to be B0.38×A _zz. The experimentalT _G ^–1 (Cu1) in YBa₂Cu₄O₈ was of the same order of magnitude as the estimated one fromT _G ^–1 (Cu2). These results appear to indicate that the electrons in the CuO₂ plane fairly spread out of the plane in both compounds.     

Re-entrant superconductivity in a magnetically ordered superconductor: La1-xGdxRu2

We have measured the critical temperature (T_c) and the upper critical magnetic field (H_c2) of La_1-xGdxRu₂. At low concentrations of the magnetic impurity (Gd), the suppression of T_c follows the expected Abrikosov-Gorkov (A-G) pair breaking curve. However, for larger concentrations, strong deviations below A-G are observed. Samples in this region (4. ? × ? 5. at. %) exhibit two T_c's. La_1-xGd_xRu₂ is known to order magnetically, probably as a spin glass, and the magnetic ordering temperature (T_M) has been measured in the normal state. This T_M curve intersects the T_c curve in the concentration range where the T_c curve is re-entrant and we therefore attribute the re-entrant T_c behavior to the magnetic ordering of the Gd³⁺ ions.     

Monte Carlo simulation of very large kinetic Ising models

We study the relaxation of Ising models in three and four dimensions aboveT _c , using multi-spin coding for lattices up to 360³ and 40⁴. The nonlinear relaxation time diverges as (T–T _c )^{–1.05±0.04} in three dimensions, where corrections to scaling are taken into account. In four dimensions the effective exponent is about 0.72; logarithmic correction factors make the analysis difficult here. The linear relaxation time for the asymptotic exponential decay is found to be larger, with effective exponents 1.31 (d=2) and 0.97 (d=4). The difference in the linear and nonlinear relaxation exponents is compatible in three dimensions with the orderparameter exponent , as predicted by Racz.Work supported by SFB 125 Aachen-Jülich-KölnWork started at Department de Physique des Systemes Desordonnes, Universite de Provence, Centre St-Jerome, F-13397 Marseille Cedex 13, France     

Temperature characteristics of heat exchange due to thermal conductivity of three hollow cylinders in their contact planes

For the case where a system of three hollow cylinders, having contact along their ends, are heated the problem on the determination of the thermal characteristics in the contact planes is solved analytically. Numerical calculations and the construction of plots of the temperature variation, thermal fluxes, and the heating and stabilization times in the contact planes are carried out on the basis of the formulas so obtained.Notation _j = (T_j–T₀)/(T₀–T_c) dimensionless temperature - T₀ initial temperature - T_c temperature of the medium - T_j temperature at an arbitrary point of the j-th cylinder - Fo_j a_jt/R ₁ ² - K_a a₂/a₁ - d R₂/R₁ - b R₁/l - _j, a_j thermal and thermiometric conductivities, respectively - R₂, R₁ respectively, the outer and inner radii of the cylinders - t time - X, Z dimensionless cylindrical coordinates Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 80–84, July, 1972.     

Ultrasonic investigation of phase transitions in K2SnCl6

The velocities and the attenuation of ultrasonic waves have been investigated as a function of temperature (255KT350K) for the cubic phase of K₂SnCl₆ which undergoes a structural transition atT _c1263K. An anomalous decrease of the shear stiffness constantc=1/2(c ₁₁ –c ₁₂) of about 30% between room temperature andT _c1 is found in this cubic high temperature phase whenT _c1 is approached from above. Whereas the softening ofc extends over a substantial temperature range (about 50 K), the other shear constantc ₄₄ shows only a weak decrease, which is an order of magnitude smaller and restricted toT–T _c110 K. NearT _c1, a strong increase occurs in the attenuation of the shear acoustic wave propagated along the [111] direction, while such an anomalous attenuation is not observed for the transverse acoustic wave propagated along [100]. Furthermore, atT _c1 a hysteresis is detected for the longitudinal sound wave velocityv _L[100], which is restricted to the temperature region 262KT263.5 K. In addition, the room-temperature elastic constants of (NH₄)₂SiF₆ and the hydrostatic pressure derivatives of the elastic constants of K₂SnCl₆ and (NH₄)₂SiF₆ at room-temperature are presented and discussed in terms of mode softening behaviour.     

Structural phase transition and internal fields in rubidium thiocyanate probed through vibrational spectroscopy

A comprehensive vibrational study of Rubidium thiocyanate (RbNCS), in the 298–448°K range reveals that the orthorhombic to tetragonal transition atT _c440°K is of order-disorder type exhibiting purely second order characteristics. A consistent order-parameter exponent 0.45±0.04 has been obtained from both Raman and IR measurements. In the Raman spectra, the appearance of sidebands in both the C–N&C–S stretching modes and their temperature dependence indicate the existence and a gradual diminution of internal electric field asT approachesT _c. These results have been discussed in the context of an anharmonic oscillator model. An activation energy (U) for the reorientational motion of NCS^– ions,U0.29±0.02 eV, has been calculated from large changes in the bandwidth (_C-N) nearT _c.     

Inhomogeneous muonium diffusion in solid nitrogen

The spin dynamics of the muonium (Mu) atom diffusing quantum mechanically in solid nitrogen (s-¹⁴N₂) has been studied using the technique of Mu spin relaxation. A strong relationship between longitudinal (T ₁ ^–1 ) and transverse (T ₂ ^–1 ) relaxation rates (familiar in NMR) has been experimentally demonstrated for the first time for muonium relaxation. At low temperatures the results are inconsistent with diffusion models using a single correlation time _c; this is taken as evidence for the intrinsic inhomogeneity of the problem. The temperature dependence of theaverage Mu hop rate _c ^–1 gives clear evidence that Mu quantum diffusion ins-N₂ is governed by the two-phonon interaction.     

Ising ferromagnet with biquadratic exchange

A spin one Ising system with biquadratic exchange, is investigated, using Green's function technique in random phase approximation (RPA). Transition temperature T_c and <(S^z)²> at T_c, are found to increase with biquadratic exchange parameter α for sc, bcc and fcc lattices. The variation of <(S^z)²> at T_c with α is found to be the same for the above lattices.     

Magnetotransport properties of a layered La1.6Ca1.4Mn2O7 polycrystal

Magnetotransport properties of a two-layered La_1.6Ca_1.4Mn₂O₇ polycrystal have been examined as a function of temperature and applied field. It was found that the magnetic transition temperature (T_c) is about 70 K higher than the insulator–metal transition temperature (T_p). Two peaks were observed on both the temperature dependence of the imaginary part of the ac magnetic susceptibility χ^′′(T ) and that of the magnetoresistance MR(T). One is slightly below T_p∼107 K and the other is near T_c∼170 K. Below 70 K, the MR ratio increases with decreasing temperature. Around and above T_p but below T_c, the magnetization shows some indication of saturation, whereas the MR ratio shows no indication of saturation. The magnetotransport properties can be explained by considering the anisotropy exchange interactions along the a–b plane and the c direction, and the low-temperature MR can be attributed to the effects of the nearly fully spin-polarized carriers’ tunneling through the insulating (La,Ca)₂O₂ layers between the adjacent MnO₂ bilayers. Received: 18 September 2000 / Accepted: 20 February 2001 / Published online: 26 April 2001     

Magnetic behaviour of Eu x (Rh1−y Fe y )3B2;x=0.6, 0.75, 1.04 andy=0.02

⁵⁷Fe ME spectra taken for Eu_x(Rh_1–yFe_y)₃B₂ compounds (x=0.6, 0.75, 1.04 and y=0.02) show quadrupole doublet and a magnetically split pattern for T < T_c ^*. Above T_c ^* the spectra merge into a single quadrupole doublet. It is seen that the addition of Fe shifts the T_c corresponding to undoped compound to T_c ^*, T_c ^*>300 K for all the three samples.     

Consolidation of hydrogenation–disproportionation–desorption–recombination processed Nd–Fe–B magnets by spark plasma sintering

We have successfully consolidated hydrogenation–disproportionation–desorption–recombination (HDDR) processed Nd–Fe–Co–Zr–B–Ga powder by spark plasma sintering (SPS). The field compacted samples were sintered at different temperatures (T_S) from 550 to 600 °C with compressive pressure of 80 MPa for 20 min. Microstructural investigations by transmission electron microscopy indicated that the sintered specimen exhibits Nd₂Fe₁₄B grains of ~300 nm with Nd-rich grain boundary phase. The optimum magnetic properties of B_r: 1.22 T, H_c: 928 kA/m, _BH_c: 600 kA/m, (BH)_max: 210 kJ/m³ were obtained in the sample sintered at 550 °C. The strategy for further improving the coercivity and remanence is discussed based on the microstructure-property relationships.     

Interfacial Adsorption in Two-Dimensional Potts Models

The interfacial adsorption W at the first-order transition in two-dimensional q-state Potts models is studied. In particular, findings of Monte Carlo simulations and of density-matrix renormalization group calculations at q=16 are consistent with the analytic result, obtained in the Hamiltonian limit at large values of q, that Wt ^–1/3 on approach to the bulk critical temperature T _c, t=|T _c–T|/T _c. In addition, the numerical findings allow to estimate corrections to scaling. Our study supports and quantifies a previous conclusion by Bricmont and Lebowitz based on low temperature expansions.     

Inelastic and quasi-elastic light scattering in (NaCN)1−x(KCN)x quadrupolar glasses

The elastic constantsc ₁₁ andc ₄₄, and the attenuation of longitudinal phonons along (100)-direction in (NaCN)_1–x(KCN)_x mixed crystals have been determined by brillouin spectroscopy in the temperature range fromT=10K–300K. Minima inc ₄₄ (T) which determine the freezing tempratureT _F in these orientational glasses appear at lower temperatures compared to neutron scattering results. The coupling of molecular reorientations to longitudinal phonons in NaCN-rich smaples shows up in dispersion effects inc ₁₁ (T) and the appearence of a dynamical central peak nearT _F .U.A. 1119 is associated to the Centre National de la Recherche Scientifique