Partition function zeros for the one-dimensional ordered plasma in Dirichlet boundary conditions

We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacity in an applied electric fieldE with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in the plane occupy the imaginary axis from –i to –i_c and i_c to i for some _c. They also occupy the diamond shape of four straight lines from ±i_c to _c and from ±i_c to –_c. The fugacity acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric fieldE. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented.     

Upper critical fields of single-crystalline and polycrystalline Ca-Sr-Bi-Cu-O compounds

The ac resistivity of a 110 K phase multiphase polycrystalline Ca-Sr-Bi-Cu-O compound and an 85 K phase single-crystalline Ca_0.9Sr_2.1Cu_2.0O_{8 +} has been measured in various magnetic fields up to 8 T. Values forB _c ^2/ (0) of 71.5 T and forB _c2 (0) of 542 T are found for the 85 K phase sample. A value forB _c2(0) of 57.9 T is estimated for the 110K phase compound.     

Critical current density of a YBa2Cu3O7 film: Comparison between experiment and collective pinning theory

With the vibrating reed technique we have measured the critical current densityJ _c of a Y 123 200 nm thin film as a function of magnetic field perpendicular to the CuO₂ planes (O T<B8 T) and temperature (20KT60 K). At fieldsB<0.1 TJ _c is magnetic field independent and decreases at higher fields. A comparison with theory indicates that a crossover from a single pinning to a small bundle collective pinning regime may explain the observed behaviour. According to our estimate the main pinning centers are weak point pins due to oxygen vacancies. From the temperature dependence ofJ _c atB0 we obtain a temperature dependence of the thermodynamical critical fieldB _c (1–T/T _c )² forT20 K which agrees with the anomalous temperature dependence ofB _c2 observed recently in highly anisotropic high temperature superconductors.     

Exact distribution of cluster size and perimeter for two-dimensional percolation

Exact series expansion data of Sykes et al. are used to calculate the average numberc _n and perimeters _n of clusters of sizen20 in the site percolation problem for the triangular, square, and honeycomb lattice. At the percolation thresholdp _n we find a sharply peaked distribution of perimeterss _n with mean s _n =((1–p _n )/p _c )n+O(n ) and width s _n ² –S _n ²n ^1.6 where1/=0.39. This perimeter s _n should not be interpreted as a cluster surface in the usual sense. Two tests confirm the universality hypothesis with reasonable accuracy. The asymptotic decay of the cluster numbersc _n withn is consistent with the postulated asymmetry aboutp _c : logc _n –n forn with1 forp<p _c and1/2 forp>p _c .     

Mössbauer study of oxygen-related lattice instabilities in oriented 1-2-3 HTSC

⁵⁷Fe Mössbauer effect measurements as a function of temperature between 78 and 293 K in grain-aligned YBaCuO (T _c=89 K, T _c<2 K) with bothc andc orientations revealed a sequence of anomalies in the recoilless fraction, center shift and linewidth of all⁵⁷Fe quadrupole doublets in the host lattice. These anomalies are believed to arise due to antiferroelectric phase transitions driven by a nonlinear anharmonic vibrational motion of oxygen atoms in a breathing mode configuration. The results obtained are indicative of a possible coexistence of high-T _c superconductivity and antiferroelectricity in 1-2-3 ceramics.     

Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Fluctuation-enhanced conductivity and magnetoconductivity of high-quality YBa2Cu3O7−δ crystals

We present measurements of the in-plane resistivity _ab of YBa₂Cu₃O_7– single crystals withT _c 92 K and _ab (100 K)50 cm. The temperature dependence of the fluctuation conductivity and of the magnetoconductivity aboveT _c is analyzed in terms of direct and indirect fluctuation contributions for layered superconductors. The combination of fluctuation conductivity and magnetoconductivity allows to determine both coherence lengths _ab (0) and _c (0) as well as the phase-relaxation time of the pairs in an unequivocal manner. Evidence for clean limit type-II superconductivity in our crystals is given by large values of the mean free pathl _{ab ab} (0).Dedicated to Prof. Dr. F. Hund on the occasion of his 95th birthday     

Ground state of a spin-phonon system. II. Adiabatic limit

The phase transition for a spin in a magnetic fieldB coupled to acoustic phonons by a coupling constant is studied. The caseB1 with an upper cutoff of unity for the phonons is studied systematically by using an adiabatic canonical transformation. In leading order the transition line is at =2/B=1. In the normal phase (<1) the ground-state energy is –B/2 plus a function of that is given explicitly as the solution of a pair theory. In the broken symmetry phase (>1) the energy is the classical energy plus the same function of =1/². It is found that the first derivatives of the energy with respect to and with respect toB have finite jumps across the transition line. Quantum fluctuations in both phases are treated. Higher-order terms are a series of powers of 1/B times functions of . The case of a small transverse fieldB is also studied. The sharp transition disappears and is replaced by rapid variation in a region of order (B₁/B)^2/3 about =1.     

Anisotropic low-temperature heat transport in YBa2Cu3O6.9 single crystal

We report measurements of the low-temperature thermal conductivity of YBa₂Cu₃O_7– (0.1) single crystals (T _c =84 K) both parallel ( ^{a, b} ) and perpendicular ( ^c ) to the CuO₂ planes. Whereas ^c (T) is found to be identical, within experimental resolution, with the phonon contribution _ph (T), ^{a, b} (T) contains an additional term linear in temperature,AT. We ascribeAT to the contribution of unpaired electronic carriers residing in the chain layers. Measurements performed in external magnetic fieldsB8 T support this interpretation. Our observations can be explained by an internal multilayer (IML) model in which it is assumed that strong superconductivity is generated within the CuO₂ layers and weak superconductivity is induced in the chain layers by the proximity effect. The fit of the experimental results to the IML model reveals that approximately 15% of the electronic carriers remain unpaired in YBa₂Cu₃O₇ belowT=1 K.     

Hydrogenated and irradiatedA15 Nb3Sn layers — Preparation,Rutherford scattering analysis,resistivity and superconductivity

Niobium films on sapphire were reacted in tin-vapour to Nb₃Sn with resistance ratiosR(297 K)/R(18.3 K) up to 6 and resistively measured superconducting transition temperaturesT _c up to 17.93 K. The composition Nb_3+z Sn_1–z H _x of electrolytically hydrogenated samples was determined depth dependent by Rutherford backscattering of 30 MeV³²S and simultaneous detection of recoiled protons. Considerable concentration gradients in the thin layers (0.27 m) were detected. The increase of resistivity with hydrogen content and the change in the temperature dependence of is analyzed. A correlation betweenT _c and ₀= is found: An increase of T _c =0.2 K at ₀25cm andx0.03 is followed by a drastic decrease toT _c <1.1 K at ₀80cm andx1. TheT _c vs. ₀ andT _c vs. (T) characteristic correlations are different from universal irradiation or preparation induced correlations. The discrepancies can be interpreted by a stiffening of phonon modes and a band-shifting caused by the hydrogen.     

Deviation of Upper Bounds of Critical Temperature of Two-Dimensional O(N) Spin Models

Critical temperature of the classical O(N) spin model in two dimensions is investigated. We show that no phase transition exists in the system if the inverse temperature is less than _c=_c(N), where _c(N) is a constant such that _c(N) > const. N log N.     

The non-relativistic limit ofP(ϕ)2 quantum field theories: Two-particle phenomena

It is proved that for two-particle phenomena theP()₂ quantum field theories with speed of lightc converge to non-relativistic quantum mechanics with a function potential in the limitc.Supported by NSF Grant No. PHY 7506746     

The Hall effect in PdSi based amorphous alloys containing Co

The Hall effect in amorphous Pd_80–x Si₂₀Co _x , wherex=8, 9, 10, 12, 15, 20 (at.% are implied throughout) alloys was investigated. The measurements were carried out at r.t. in fields up to 17·5 kGauss. The variation of the Hall fieldE _H vs magnetic fieldB shows features typical for bulk ferromagnetics. The Hall constantR ₁ describing the extraordinary effect ranges from 0·29 to 27·64 (×10^–/4 in cm³/A. sec both) reaching its maximum value for the alloy withx= =12. The interpretation of theE _H vsB curves obtained is based on a model with magnetic clusters carrying giant magnetic moments. These clusters are considered to have close relation to the clusters observed by electron microscopy. Magnetic moment of an average magnetic cluster is estimated to be of the order of 1000 _B for the alloys with more than 9 at.% Co.     

Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place.     

On the asymptotic behaviour of infinite gradient systems

We consider gradient systems of infinitely many particles in one-dimensional space interacting via a positive invariant pair potential with a hard core. The main assumption is that is strictly convex within the rangeR of (whereR is a fixed number ). Under some technical conditions we prove the following theorems: Let the initial distribution be given by a translation invariant point process onR ¹. Then there exists only one extreme equilibrium state with a given intensityI() satisfyingI()R ^–1, and all ergodic initial distributions with an intensityI()R ^–1 converge weakly ast to the extreme equilibrium state with the same intensity.     

Flux diffusion in high-T c superconductors

In type-II superconductors in the flux flow (J J _c ), flux creep (J _c J _c ), and thermally activated flux flow (TAFF) (J J _c ) regimes the inductionB(r,t), averaged over several penetration depths , in general follows from a nonlinear equation of motion into which enter the nonlinear resistivities (B, J ,T) caused by flux motion and (B, J ,T) caused by other dissipative processes.J andJ are the current densities perpendicular and parallel toB,B=|B|, andT is the temperature. For flux flow and TAFF in isotropic superconductors with weak relative spatial variation ofB, this equation reduces to the diffusion equation plus a correction term which vanishes whenJ =0 (this means B××B=0) or when – = 0 (isotropic normal conductor). When this diffusion equation holds the material anisotropy may be accounted for by a tensorial . The response of a superconductor to an applied current or to a change of the applied magnetic field is considered for various geometries. Such perturbations affect only a surface layer of thickness where a shielding current flows which pulls at the flux lines; the resulting deformation of the vortex lattice diffuses into the interior until a new equilibrium or a new stationary state is reached. The a.c. response, in particular the frequency with maximum damping, depends thus on the geometry and size of the superconductor.     

Ising Models on Hyperbolic Graphs II

We consider Ising models with ferromagnetic interactions and zero external magnetic field on the hyperbolic graph (v, f), where v is the number of neighbors of each vertex and f is the number of sides of each face. Let T _c be the critical temperature and T _c =supTT _c: ^f=( ⁺+ ^–)/2, where ^f is the free boundary condition (b.c.) Gibbs state, ⁺ is the plus b.c. Gibbs state and ^– is the minus b.c. Gibbs state. We prove that if the hyperbolic graph is self-dual (i.e., v=f) or if v is sufficiently large (how large depends on f, e.g., v35 suffices for any f3 and v17 suffices for any f17) then 0<T _c <T _c, in contrast with that T _c =T _c for Ising models on the hypercubic lattice Z ^d with d2, a result due to Lebowitz.⁽²²⁾ While whenever T<T _c , ^f=( ⁺+ ^–)/2. The last result is an improvement in comparison with the analogous statement in refs. 28 and 33, in which it was only proved that ^f=( ⁺+ ^–)/2 when TT _c and it remains to show in both papers that ^f =( ⁺+ ^–)/2 whenever T<T _c . Therefore T _c and T _c divide [0, ] into three intervals: [0, T _c ), (T _c , T _c), and (T _c, ] in which ^{+ –} but ^f =( ⁺+ ^–)/2, ^{+ –} and ^f ( ⁺+ ^–)/2, and ⁺= ^–, respectively.     

Infrared lattice bands of some pearls

From analysis of anisotropical lattice bands properties of 50 reflection spectra both of the CO stretching and bending bands measured from some pearl (Ca⁺⁺CO ₃ ^–– or Ca⁺⁺HCO ₃ ^–– layer) we discussed following subjects.i) Quantized properties present both in reflectivity and in energy. ii) classifications of the Optical Activity. iii) Polar distributions of the CO₃ oscillators in Ca⁺⁺CO ₃ ^–– surface mono-layer. iv) Force constants of these oscillators. v) Step variation of the dipolemoment and their influences to the degree of Optical Activity. vi) Two types of hysteresis loops of the values of Y_N (M_2Jbend ()/M_1Jstret. ()) derived from the oscillators which are at innert-state, at weak active-state and at active-state.     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .