Long-wavelength behavior of the optimal HNC/0 solution for the ground state

The ground-state wave function for a two-dimensional homogeneous liquid⁴He at zero temperature is obtained from a paired-phonon analysis within the HNC/0 approximation. The long-wavelength behavior of the two-body correlation factor,u(q), is studied by following the procedure previously applied to three-dimensional bulk systems. It is shown that a cut-off law for the phonons can be determined by analyzingu(q) at small two-dimensional momentaq. The numerical results strongly support an exponential cut-off similar to that suggested by Chester and Reatto for the bulk liquid. The first-sound velocityc ₁ and the cut-off momentumq _c are calculated at several densities in the range 0.028–0.080 Å^–2.     

Growth of clusters in a first-order phase transition

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59T _c, whereT _c is the critical temperature, and the concentration of minority atoms was=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc ₁(1-)³ w(t),c ₁ (1–)⁴ Q _l w(t)^l(2l10); wherec _l is the concentration of clusters of sizel;Q ₂,...,Q ₁₀ are known constants, the cluster partition functions;t is the time; andw(t)=0.015(1+7.17t ^–1/3). The distribution of large clusters (l20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c _l ,(t)=–(d/dl) [lnt+p (l/t)], where is a function given by those authors and is defined by(x)=C _o e–x-C ₁ e ^–4x/3-C ₂ e ^–5x/3;C ₀,C ₁,C ₂ are constants determined by considering how the total number of particles in large clusters changes with time.Supported by the U.S. Air Force Office of Scientific Research under Grant No. 78-3522 and by the U.S. Department of Energy under Contract No. EY-76-C-02-3077*000.     

A new structure of In-based ohmic contacts ton-type GaAs

Electrical, structural and reaction characteristics of In-based ohmic contacts ton-GaAs were studied. Attempts were made to form a low-band-gap interfacial phase of InGaAs to reduce the barrier height at the metal/semiconductor junction, thus yielding low-resistance, highly reliable contacts. The contacts were fabricated bye-beam sputtering Ni, NiIn and Ge targets on VPE-grownn ⁺-GaAs film (1 m, 2 × 10¹⁸ cm^–3) in ultrahigh vacuum as the structure of Ni(200 Å)/ NiIn(100 Å)/Ge(40 Å)/n ⁺-GaAs/SI-GaAs, followed by rapid thermal annealing at various temperatures (500–900°C). In this structure, a very thin layer of Ge was employed to play the role of heavily doping donors and diffusion limiters between In and the GaAs substrate. Indium was deposited by sputtering NiIn alloy instead of pure In in order to ensure In atoms to be distributed uniformly in the substrate; nickel was chosen to consume the excess indium and form a high-temperature alloy of Ni₃ln. The lowest specific contact resistivity ( _c) of (1.5 ± 0.5) × 10^–6 cm² measured by the Transmission Line Method (TLM) was obtained after annealing at 700°C for 10 s. Auger sputtering depth profile and Transmission Electron Microscopy (TEM) were used to analyze the interfacial microstructure. By correlating the interfacial microstructure to the electronical properties, In _x Ga_{1– x}As phases with a large fractional area grown epitaxially on GaAs were found to be essential for reduction of the contact resistance.This work was supported by the National Natural Sciences Foundation of China (NSFC)     

Decay of the Two-Point Function in One-Dimensional O(N) Spin Models with Long-Range Interactions

Using Griffiths and Lieb–Simon type inequalities, it is shown that the two-point function of ferromagnetic spin models with N components in one dimension decays like the interaction J(n)n ^– provided that 1N4 and T>T _c.     

Temperature anomalies in the dispersion and absorption of sound near phase transition points at low temperatures

We examined the attenuation and dispersion of sound during phase transitions with an overdamped soft mode at low temperatures. The obtained temperature and frequency dependences differ from results known at the high-temperature asymptote. The temperature anomalies are sharper. At low frequencies, the attenuation behaves like (T – T_c)^–5/2 for a critical phonon spectrum isotropic in k, and like (T–T_c)^–2 for uniaxial ferroelectrics. The presence of a temperature anomaly is characteristic also for high-frequency attenuation, behaving like (T–T_c)^–1/2 and ln(T–T_c)., respectively. We discuss briefly the results obtained from an experimental test.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 70–74, January, 1989.     

Internal Lifschitz singularities of disordered finite-difference Schrödinger operators

The integrated density of states has C-like singularities, ln|k(E)–k(E _c )|=–|E–E _c |^–v/2 _c (E), with _c >0, a milder function at the edges of the spectral gaps which appear when the distribution function of the potentiald has a sufficiently large gap. The behaviour of _c nearE _c is determined by the local continuity properties ofd near the relevant edge: _c (E)=O(1) ifd has an atom and =O(ln|E–E _c |) if is (absolutely) continuous and power bounded.     

Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by _t =2 fort=2, 3,. Scaling theory predicts thatP _p (¦C ₀¦S(p))–(p _c –p) andE _p (1/¦C ₀¦; ¦C ₀¦S(p))–(p _c –p)³, whereS(p) is the typical cluster size. It is found that (p _c –p)P _p (|C ₀S(p) ^1–)(p _c –p)^1–2 and (p _c –p)³E _p (1/|C ₀|;|C ₀|S(p) ^1–))(p _c –p)^3–4.     

Correlation betweenJ c and screw dislocation density in sputtered YBa2Cu3O7-δ films

Electric transport properties of sputtered YBa₂Cu₃O_7– films were studied as a function of screw dislocation density, ranging from 5·10⁷ cm^–2 to 1.3·10⁹ cm^–2 as determined at the film surface. A correlation was found between the number of screw dislocations and the critical current density (J _c ). Films with higher screw dislocation densities have higher critical current densities and a slower drop ofJ _c as a function of applied magnetic fieldH.     

Mean-Field Critical Behavior for the Contact Process

The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()– _c as _c and ()( _c–)^–1 as _c, where () and () are the spread probability and the susceptibility of the infection respectively, and _c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.     

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.     

An interaction of nucleons at an energy between 1014 and 1015 eV/nucleon

A jet (0+14) with primary energy {3.3 _{– 2.2} ^{+ 5.3} }. 10¹⁴ eV/nucl. was observed in the I-stack. An interaction with very small multiplicity (n _s =3or 4)found in the axis of the jet is probably caused by another nucleon from the -primary. 10 particles of the narrow cone have opening angles of some 10^–4 radians, 4 particles in the diffuse cone are emitted at angles of a few 10^–2 radians. A pronounced anisotropy exists in the C. M. system. The coefficient of inelasticity 0.1was calculated directly extrapolating the measured energies of secondaries. The interpretation of the whole event is in good agreement with Heisenberg's theory of multiple production of particles.     

A uniqueness condition for Gibbs measures,with application to the 2-dimensional Ising antiferromagnet

A uniqueness condition for Gibbs measures is given. This condition is stated in terms of (absence of) a certain type of percolation involving two independent realisations. This result can be applied in certain concrete situations by comparison with ordinary percolation. In this way we prove that the Ising antiferromagnet on a square lattice has a unique Gibbs measure if (4–|h)<1/2ln(P _c /(1–P _c )), whereh denotes the external magnetic field, the inverse temperature, andP _c the critical probability for site percolation on that lattice. SinceP _c is larger than 1/2, this extends a result by Dobrushin, Kolafa and Shlosman (whose proof was computer-assisted).The research which led to this paper started while the author was at Cornell University, partly supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University     

Measurements of the refractive indices and refractive index increment of a synthetic PMMA solutions at 488 nm

We describe a Mach–Zehnder interferometer (MZI) method for measuring the refractive index (RI) of polymethyl-methacrylate (PMMA) solution in both acetone and methyl-ethyl-ketone (MEK). The measurements are made as a function of concentration values 4, 8, 12, 16 and 20 g/l at a wavelength of 488 nm with a high degree of accuracy tends to 1.4×10⁻⁵. The refractive index increments (RIIs) dn/dc of PMMA in both investigated solvents are determined too. In addition, the RIIs Δn as a function of concentration and the RIIs at zero concentration (dn/dc)_c=0 are determined for both solvents accurately. The PMMA solutions in acetone and MEK solvents are chosen for laser light scattering investigations.     

Note on the susceptibility exponent for two-dimensional percolation

Analyses of mean site content, mean bond content, mean perimeter and related quantities give a susceptibility diverging as (p _c –p)^–, with 2.41±0.025. This exponent disagrees with some earlier estimates but it is consistent with the (p _c –p)^–2.388... divergence predicted by the formulas of den Nijs, Nienhuis et al. and Pearson.     

The tortuosity of occupied crossings of a box in critical percolation

We consider the length of an occupied crossing of a box of size [0,n]×[0, 3n] ^D–1 (in the short direction) in standard (Bernoulli) bond percolation on ^D at criticality. Let ¦s _n¦ be the length of the shortest such crossing. It is believed that ¦s _n¦ ^1+c in some sense for somec>0. Here we show that if the correlation length(p) satisfies (p)p _c}–p) ^– for some <1, then with a probability tending to 1, ¦s _n¦>/C ₁ n ^1/(logn)^–(1–)/. The assumption (p)C ₃(p _c–p)^– with <1 has been rigorously established^(1,2) for largeD, but cannot hold⁽³⁾ forD=2. In the latter case, let ¦l _n¦ be the length of the lowest occupied crossing of the square [0,n]². We outline a proof ofP _pc(¦l_n¦ n ^1+c)n ^– for somec, >0. We also obtain a result about the length of optimal paths in first-passage percolation.     

Comparative study of the specific heat of superconducting and non-superconducting YBa2Cu3O7−x

We have measured the specific heat, the electrical resistance and the magnetic susceptibility of YBa₂Cu₃O_7–x in a superconducting (sc) and in a non-superconducting (nsc) version. The latter was obtained by inducing a small loss of oxygen. In the sc sample we find a jump of the specific heat with C=3.6 J mole^–1 K^–1. Below the maximum nearT _c the specific heat of the sc version drops too fast for an electronic effect alone: there is a cross-over from excess to deficiency already at 0.9T _c . The specific heat of the nsc version shows a change of slope in the temperature range between 70 and 80 K, which indicates the existence of a second specific heat anomaly, which apparently exists independently of that due to the onset of superconductivity and explains at least partially the premature crossover.Alexander von Humboldt fellow. On leave in absence from Centro Atomico Bariloche—CNEA Argentina     

Higher-order susceptibilities of the regular and the random Ising model on the Cayley tree. I

Explicit expressions for the fourth-order susceptibility (⁴), the fourth derivative of thebulk free energy with respect to the external field, are given for the regular and the random-bond Ising model on the Cayley tree in the thermodynamic limit, at zero external field. The fourth-order susceptibility for the regular system diverges at temperature T _c ⁽⁴⁾ = 2k _B ^–1 J/ln{1+2/[(z–1)^3/4–1]}, confirming a result obtained by Müller-Hartmann and Zittartz [Phys. Rev. Lett. 33:893 (1974)]; Herez is the coordination number of the lattice,J is the exchange integral, andk _B is the Boltzmann constant. The temperatures at which ⁽⁴⁾ and the ordinary susceptibility (²) diverge are given also for the random-bond and the random-site Ising model and for diluted Ising models.     

High-density percolation: Exact solution on a Bethe lattice

A new percolation problem is posed where the sites on a lattice are randomly occupied but where only those occupied sites with at least a given numberm of occupied neighbors are included in the clusters. This problem, which has applications in magnetic and other systems, is solved exactly on a Bethe lattice. The classical percolation critical exponents=gg=1 are found. The percolation thresholds vary between the ordinary percolation thresholdp _c (m=1)=l/(z – 1) andp _c(m=z) =[l/(z – 1)]¹/(z–1). The cluster size distribution asymptotically decays exponentially withn, for largen, p p _c .Supported in part by National Science Foundation grant DMR78-10813.     

Special energies and special frequencies

Special frequencies have been asserted to be zeros of the density of frequencies corresponding to a random chain of coupled oscillators. Our investigation includes both this model and the random one-dimensional Schrödinger operator describing an alloy or its discrete analogue. Using the phase method we exactly determine a bilateral Lific asymptotic of the integrated density of statesk(E) at special energiesE _s , which is not only of the classical type exp(–c/|E–E _s |^1/2) but also exp(–c/|E–E _s |) is a typical behaviour. In addition, other asymptotics occur, e.g. |E–E _s | ^c , which show thatk(E) need not bek .     

The broken supersymmetry phase of a self-avoiding random walk

We consider a weakly self-avoiding random walk on a hierarchical lattice ind=4 dimensions. We show that for choices of the killing ratea less than the critical valuea _cthe dominant walks fill space, which corresponds to a spontaneously broken supersymmetry phase. We identify the asymptotic density to which walks fill space, (a), to be a supersymmetric order parameter for this transition. We prove that (a)(a _c–a) (–log(a _c–a))^1/2 asaa _c, which is mean-field behavior with logarithmic corrections, as expected for a system in its upper critical dimension.Research partially supported by NSF Grants DMS 91-2096 and DMS 91-96161.