Nontrivial critical behaviour in a lattice model of random surfaces

A model of “planar random surfaces without spikes” on hypercubical lattices was introduced some years ago as a discretization of quantum string theory. We review some general properties of this model and present results from a Monte Carlo study of its critical behaviour in d = 4, 8 and 10 dimensions. In d = 4 dimensions we find a Hausdorff dimension d_H ≈ 4 and an anomalous dimensions η ≈ 1. These critical exponents imply a deviation from mean field theory in contrast to other lattice random surface models. Furthermore, we find evidence for mean field behaviour in 8 and 10 dimensions, indicating an upper critical dimension d_c^u ⩽ 8.     

Anisotropic supergravity cosmologies

Anisotropic cosmologies of Bianchi types I, II, VI₀, VII₀, VIII and IX are studied in the bosonic sector of d = 11 supergravity. Exact solutions are given for all types in s = 4 dimensions coupled to the “round” (d ? s = 7) seven-sphere solutions due to Freund, Rubin, Duff and Pope, and Englert. The generalized Kasner, the Taub-NUT-de Sitter and some “mixmaster” solutions with a cosmological constant are derived. In addition, we wish to point out that the isotropic solution given recently by Myung and Kim does not exist. Another inconsistent solution was also given by Gleiser et al.     

Strict monotonicity for critical points in percolation and ferromagnetic models

When is the numerical value of the critical point changed by an enhancement of the process or of the interaction? Ferromagnetic spin models, independent percolation, and the contact process are known to be endowed with monotonicity properties in that certain enhancements are capable of shifting the corresponding phase transition in only an obvious direction, e. g., the addition of ferromagnetic couplings can only increase the transition temperature. The question explored here is whether enhancements do indeed change the value of the critical point. We present a generally applicable approach to this issue. For ferromagnetic Ising spin systems, with pair interactions of finite range ind?2 dimensions, it is shown that the critical temperatureT _c is strictly monotone increasing in each coupling, with the first-order derivatives bounded by positive functions which are continuous on the set of fullyd-dimensional interactions. For independent percolation, with 0<p _c<1, we prove that any “essential enhancement” of the process has an effect on the critical probability, a result with applications to the question of the existence of “entanglements” and to invasion percolation with trapping.     

Supersymmetric extended solitons

It is shown that the recently classified “super p-brane” actions can be considered as effective actions “extended solitons” of supersymmetric field theories for which a Bogomol'nyi-type bound of the form (mass/unit p-volume) ⩾ topological charge is saturated. Such solutions can be found by “double-dimensional oxidation” of the instanton solutions of supersymmetric field theories in d = 1, 2, 4 spacetime dimensions. These provide a field-theoretic of all super p-branes except the d = 10 superstring and the d = 11 supermembrane.     

Finite-size corrections to the free energy of Coulomb systems with a periodic boundary condition

Classical Coulomb systems ind dimensions (d?2) with a periodic boundary condition, periodW, in the directionx ^(d)are considered. With the other directions of the confining volume of lengthL, it is shown that if the system is in a conducting phase, then the “strip” free energykTf _W ,f _W = ?lim _L→∞ L ^?(d?1) log Z, has the large-W expansion $$f_W \sim Wf_\infty + \frac{{(d/2 - 1)\Gamma (d/2 - 1)}}{{\pi ^{d/2} W^{d - 1} }}\zeta (d) + O\left( {\frac{1}{{W^{d + 1} }}} \right)$$ wherekTf _∞ is the bulk free energy per unit volume, ζ(x) denotes the Riemann zeta function, andΓ(x) denotes the gamma function. With 1/W identified askT, this result is precisely the low-temperature behavior of the free energy of a (d?1)-dimensional Debye solid. This fact is explained in terms of an equivalence between the Coulomb gas and quantum fields. Also, the expansion is verified for some exactly solved models of Coulomb systems in two dimensions.     

Optical solitons in dense resonant media

Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times (T _p ? T ₁, T ₂), and “incoherent,” where the pulse duration falls between the relaxation times (T ₂ ? T _p ? T ₁). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.     

Warp factors and extended sources in two transverse dimensions

We study the solutions of the Einstein equations in (d+2)-dimensions, describing parallel p-branes (p=d−1) in a space with two transverse dimensions of positive gaussian curvature. These solutions generalize the solutions of Deser and Jackiw of point particle sources in (2+1)-dimensional gravity with cosmological constant. Determination of the metric is reduced to finding the roots of a simple algebraic equation. These roots also determine the nontrivial “warp factors” of the metric at the positions of the branes. We discuss the possible role of these solutions and the importance of “warp factors” in the context of the large extra dimensions scenario.     

The microwave spectra of ortho-fluorotoluene with the asymmetric internal rotors CH2D and CD2H

The rotational spectra of αd₁- and αd₂-ortho-fluorotoluene in the ground state of the methyl group torsion have been measured. The evaluation of the spectra has been based on the theory for the internal rotation of an asymmetric internal top formulated earlier by several authors. The barrier potential being threefold symmetric (V₃), each torsional level consists of three nondegenerate substates, designated as sy and ±asy. The sy-state is assigned to the conformation with the unique methyl hydrogen isotope within the molecular heavy-atom plane (sy-rotamer), while the ±asy-states belong to the respective out-of-plane conformation (asy-rotamer). In the torsional ground state the level spacing between the ±asy substates is very small and numerous accidental close degeneracies are present between the rotational level systems based on these torsional substates. The rotational levels involved are strongly perturbed by the coupling between molecular overall rotation and internal rotation. Large deviations from a rigid rotor spectrum and (+) ? (?) intersystem (“tunneling”) transitions are observed. The spectrum of the asy-rotamer can be well reproduced by a “two-dimensional” Hamiltonian containing 11 “rotational constants,” 9 of which are determined by a fit to the spectrum. Several are sufficiently barrier-dependent to derive V₃. We obtain (in cal/mole) 567 ± 48 for αd₁-ortho-fluorotoluene, 711 ± 40 for the αd₂-isotope. The deviations from 649 cal/mole for the normal isotope are appreciable, probably indicating shortcomings of the semirigid model. The sy-rotamer presents a rigid rotor spectrum.     

The Wigner transition as a bifurcation

The Wigner transition from a low-density electron gas to an “electron solid” is described as a second-order phase transition. Using bifurcation theory, the corresponding critical mean interelectron spacing is found to lie in the range 3.92 < d_c/a_o ? 6.03.     

Effect of local atomic phase separation in the x-ray absorption near edge structure spectroscopy of FeSexTe1−x

Ab initio X-ray absorption near edge structure (XANES) calculations for FeSe_xTe_1−x, using a structural model that combines FeSe and FeTe phases at the nanoscale, are compared with Fe K-edge XANES measurements in the “pre-edge” region. The important aspects of this model are (i) magnetic order in the FeTe phase; (ii) Se and Te atoms placed randomly in both FeSe and FeTe crystallographic positions and; (iii) the two distinct distances for Fe–Se and Fe–Te of the bulk phases. The calculated spectra reproduce the observed increase of spectral weight in the experiments on FeSe_xTe_1−x with Se concentration. This is consistent with an inhomogeneous local electronic structure of FeSe_xTe_1−x. Additionally, we have calculated projected electronic density of d-states for the Fe atom, revealing increased spectral weight in the “pre-edge” region of the XANES spectra, which correlates with the increase in Se concentration. The decrease of calculated Fe d-density of states for the Fermi level, N(ε_F), for high Te content is consistent with the suppression of superconductivity in the title system.     

ESR- and magnetic susceptibility measurements on the potassium molybdenum bronzes

Magnetic and transport properties of the transition metal bronzes are determined by the extent of delocalization of the transition metal 4d-electrons. We report on ESR investigations of single crystals of the “red” potassium molybdenum bronze K_0.33MoO₃ and of the “blue” potassium molybdenum bronze K_0.30MoO₃. ESR spectra due to unpairedd-electrons are observed at both compounds. Analyzing the hyperfine structure we find that thed ¹-electrons are delocalized over six molybdenum lattice sites in semiconducting K_0.33MoO₃. The same K_0.33MoO₃ crystals show another spectrum which is caused by pairs of exchange coupledd-electrons. Our results are compared with those from magnetic susceptibility measurements and are discussed in connection with the crystal structure of K_0.33MoO₃ and K_0.30MoO₃.     

Investigation of a single barrier discharge in submillimeter air gaps. Nonuniform field

Pulse characteristics of single barrier discharges as well as parameters of charges accumulated on the surface of a dielectric under the atmospheric pressure in the “needle-(0.1–2.0)-mm air gap-polymer barrier-plane” system are investigated. It is found experimentally that for the positive polarity of the needle, the voltage for the discharge initiation is higher than in the case of the negative polarity by ～25–35%. The reversal of the needle polarity from negative to positive increases the amplitude of the discharge current and the accumulated surface charge by ～1.5–3 times. For the positive polarity of the needle, the discharge is governed by a streamer mechanism, while for the negative polarity, the discharge is initiated by the formation of a single Trichel pulse. The single pulse regime is observed for the discharge current up to a certain electrode gap d _CR. For the positive needle and for air gap width d _air > d _CR ≈ 1.5 mm, a multipulse burst corona is formed, while for the negative needle and d _air > d _CR ≈ 0.9 mm, a damped sequence of Trichel pulses evolves in the system.     

Quantizing a classically ergodic system: Sinai's billiard and the KKR method

Sinai's “billiards on a torus,” i.e., free motion of a particle in a plane amongst reflecting discs of radius R centred on points of the unit square lattice, is a classically ergodic system with two freedoms, parametrized by R. Quantal energy levels E_n are given by the vanishing of the Korringa-Kohn-Rostoker (KKR) determinant of solid state theory. This gives a rapid computational scheme for computing E_n as functions of R. Except for the integrable case R = 0, no degeneracies are found, illustrating the theorem that two parameters, not one, are required to make levels cross in a generic system. The same theorem leads to the prediction that the probability distribution of the spacings S of neighbouring levels is $\text{O}$(S) as S → 0, in good agreement with computation. The KKR determinant is transformed analytically to give the level density d(E) semiclassically (i.e., as ? → 0) as the sum of a steady contribution $\text{d}\text{?}\text{(E)}$ and an oscillatory contribution d_osc(E). $\text{d}\text{?}$ is $\text{O}$(?^?2) and is given by the Weyl “area” formula plus “edge,” “corner” and “curvature” corrections, in excellent agreement with computation. d_osc is given by a sum over classical closed orbits (all unstable). Nonisolated closed orbits (not hitting discs) contribute terms with $\text{O}$$\text{(?}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext><mtext>)</mtext>}}$ to d_osc, while isolated closed orbits (bouncing between discs) contribute terms with $\text{O}$(?^?1) to d_osc. The isolated orbits are vastly more numerous than the nonisolated orbits and their contributions cannot be neglected. As a means of calculating the individual E_n (rather than the smoothed spectrum), the KKR method is much more efficient than the classical path sum.     

Multiscale approach to micro/macro fatigue crack growth in 2024-T3 aluminum panel

When two contacting solid surfaces are tightly closed and invisible to the naked eye,the discontinuity is said to be microscopic regardless of whether its length is short or long.By this definition,it is not sufficient to distinguish the difference between a micro-and macro-crack by using the length parameter.Microcracks in high strength metal alloys have been known to be several centimeters or longer.Considered in this work is a dual scale fatigue crack growth model where the main crack can be micro or macro but there prevails an inherent microscopic tip region that is damaged depending on the irregularities of the microstructure.This region is referred to as the"micro-tip"and can be simulated by a sharp wedge with different angles in addition to mixed boundary conditions.The combination is sufficient to model microscopic entities in the form of voids,inclusions,precipitations,interfaces,in addition to subgrain imperfections,or cluster of dislocations.This is accomplished by using the method of"singularity representation"such that closed form asymptotic solutions can be obtained for the development of fatigue crack growth rate relations with three parameters.They include:(1)the crack surface tightness*represented by o/=0.3-0.5 for short cracks in region I,and 0.1-0.2 for long cracks in region II,(2)the micro/macro material properties reflected by the shear modulus ratio*(=micro/macro varying between 2 and 5)and(3)the most sensitive parameter d*being the micro-tip characteristic length d*(=d/do)whose magnitude decreases in the direction of region I II.The existing fatigue crack growth data for 2024-T3 and 7075-T6 aluminum sheets are used to reinterpret the two-parameter da/dN=C(K)nrelation where K has now been re-derived for a microcrack with surfaces tightly in contact.The contact force will depend on the mean stress m or mean stress ratio R as the primary parameter and on the stress amplitude a as the secondary parameter.     

Supergravity,the seven-sphere,and spontaneous symmetry breaking

N = 1 supergravity in d = 11 dimensions spontaneously compactifies on S⁷ to an N = 8 supergravity in d = 4 with a local SO(8) × SO(8) invariance, probably enlargeable to SO(8) × SU(8). Apart from group manifolds, S⁷ is the only compact manifold to admit an absolute parallelism. This permits (a) a “squashing” of S⁷ which gives expectation values to the scalar fields and (b) a parallelizing “torsion” which gives expectation values to the pseudoscalars. This correspondence between extrema of the d = 4 effective potential and solutions of the d = 11 field equations provides a Kaluza-Klein origin for the spontaneous breakdown of gauge symmetries, discrete symmetries, and supersymmetries. It also puts a new perspective on the puzzle of the cosmological constant.     

Magnets with random uniaxial anisotropy: Thermodynamic properties in the large-N limit

We show that the random-axis model lends itself to a systematic large-N calculation. The model shows different behavior below and above four dimensions. The equation of state is derived and discussed in terms of “Arrott” plots. Higher-order terms in the disorder, when summed, have a crucial effect on the susceptibility which is found to be finite below four dimensions (and above four dimensions for strong disorder). A spin-glass to paramagnetic phase transition is characterized by the vanishing of the Edwards-Anderson order parameter, which differs from zero in the spin-glass phase. A cusp in the specific-heat and susceptibility is seen across the transition. The cross-over exponent and other exponents of interest are calculated. Above four dimensions a third phase appears for weak disorder and low-temperature ferromagnetic in nature. The transverse and longitudinal susceptibilities are discussed. Whereas the ferromagnetic transition is characterized by mean-field exponents, the ferromagnetic to spin-glass exponents are equal to their counterparts in the non-random system in d ? 2 dimensions. This is shown to originate from an effective random field proportional to the EA order parameter. The flow equations in the large-N limit are also discussed.     

Separation of S-wave pseudoscalar and pseudovector amplitudes in π−P↑ → π+π−n reaction on polarized target

A new analysis of S-wave production amplitudes for the reaction π^?p↑ → π⁺π^?n on a transversely polarized target is performed. It is based on the results obtained by the CERN-Cracow-Munich collaboration in the ππ energy range from 600 MeV to 1600 MeV at 17.2 GeV/c π^? momentum. Energy-independent separation of the S-wave pseudoscalar amplitude (π exchange) from the pseudovector amplitude (a ₁ exchange) is carried out using assumptions much weaker than those in all previous analyses. We show that, especially around 1000 MeV and around 1500 MeV, the a₁ exchange amplitude cannot be neglected. The scalarisoscalar ππ phase shifts are calculated using fairly weak assumptions. Below the KK? threshold we find two solutions for the π — π phase shifts, for which the phases increase slower with the effective π — π mass than the P-wave phases. Both solutions are consistent with a broad f ₀(500) but only one is similar to the well-known “down” solution. We find also the third solution (with a somewhat puzzling behavior of inelasticity) which exhibits a narrow f ₀(750) claimed by Svec. All the solutions undergo a rapid change at the KK? threshold. Above 1420 MeV the phase shifts increase with energy faster than those obtained without the polarized-target data. This phase behavior as well as an increase of the modulus of the a₁-exchange amplitude can be due to the presence of the f ₀(1500).     

Implications of an ionic model of SiO2

As a test of an ionic model of SiO₂, we have computed the silicon Kβ and L_2,3 X-ray emission bands using ionic wave functions for idealized β-cristobalite and results from an earlier tight-binding fit to the valence bands. Good agreement with experiment is obtained except for a high energy feature in the L_2,3 spectrum. It is noted that the “ionic” O^2? wave functions are very diffuse and have considerable amplitude on neighboring sites. Orthogonalization to silicon s and p cores leads to 3s and 3p-like behavior about the silicons; however, there is no d core to orthogonalize to, so the d-like behavior about the silicons is not properly described. Some explict 3d admixture appears necessary to describe the upper L_2,3 feature. The Compton scattering results of Rosenberg et al. are discussed in the context of our results.     

Phase diagrams of weakly anisotropic Heisenberg antiferromagnets: III. Nonlinear excitations and random fields in quasi 2-dimensional systems

The concept of effective field-dependent anisotropy is applied to the “spinflop” transition in the quasi 2-d Heisenberg antiferromagnet with weak orthorhombic anisotropy. From the correspondence between the “spinflop” problem and the commensurate-incommensurate transtion it follows that the “spinflop” is not first order and that random fields may cause domain-wall formation. This would explain the observed broadening of the “spinflop” in K₂MnF₄. In 3-d antiferromagnets such anomalous broadening is not observed, which would agree with the critical dimensionality d_c = 2 for the random-field problem.