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.     

A μSR study of spin density wave condensation in Cr85Mo15

Zero field SR spectra from Cr₈₅Mo₁₅ are well described by the sum of a lightly damped (0.02s^–1<₁<0.2s^–1) and a heavily damped (2s^–1<₂<15s^–1) exponential. The temperature dependence of these components is discussed in relation to the condensation of the incommensurate spin density wave and the onset of the antiferromagnetic state in this Cr-like alloy below T_N=120K. Evidence is presented for the nucleation of the spin density wave at temperatures greater than 1.5T_N.     

Scaling function for energy-density correlations: Dispersion theory andε-expansion forT>T c

A dispersion representation for the static energy-density correlation function ² (q) ²(–q) _c =C(q,T)=A+Bt ^–h(z ²), wherez=q , t=(T—T)_c/T _c and is the correlation length, is discussed.h(z ²) is calculated to order ² in the zero-field critical region (T>T _c) for the standard isotropicn-component ⁴Ginzburg-Landau-Wilson model. Utilizing a procedure similar to that introduced by Bray for the two-point correlation function, the-expansion results are used in conjunction with an approximant for the spectral functionF(z/2) Imh(—z ²) based on the asymptotically exact short-distance expansion resulth ^–1(z ²)z ^/v[D ₀+D ₁ z ^{–(1 —)/v} +D ₂ z ^–1/v ] to predict quantitatively the full momentum dependence ofC(q,T) forT>T _c. In contrast to the two-point correlation function,C(q,T) is found to be a monotonic function as the critical temperature is approached at fixedq (forT>T _c).     

Long-Time tails in a random diffusion model

Letw = {w(x)xZ^d} be a positive random field with i.i.d. distribution. Given its realization, letX _t be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w^–1(X_t). The processX={X _t:t0} combined withw on a common probability space is an example of random walk in random environment. We consider the quantities _t =(d/dt) E (X _t ² –M ^–1 t and _t(w) = (d/dt)E_w(X _t ² – M^– 1t). Here E_w. is expectation overX at fixedw and E = E_w (dw) is the expectation over bothX andw. We prove the following long-time tail results: (1) lim_t t^d/2_t= V²M^d/2–3(d/2)^d/2 and (2) lim_t t^d/4 _st(w)= Z_s weakly in path space, with {Z_s:s>0} the Gaussian process with EZ_s=0 and EZ_rZ_s= V²M^d/2–4(d)^d/2 (r + s)^–d/2. HereM and V² are the mean and variance of w(0) under . The main surprise is that fixingw changes the power of the long-time tail fromd/2 tod/4. Since , with ₀ the stationary measure for the environment process, our result (1) exhibits a long-time tail in an equilibrium autocorrelation function.     

Self-consistent calculation of statics and dynamics of the roughening transition

Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT _R is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h ² are found to behave—lnFlnh ²(T _R –T)^–1 for temperaturesT approachingT _R from below. The linear relaxation rate of the order parameter is found to be proportional to ^–2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference aboveT _R , shows a metastable regime belowT _R with a spinodal limit of metastability _c , beyond which oscillatory growth starts. The critical behavior of _c is found to be ln _c –(T _R –T)^–1+O(ln (T _R –T)).     

Smooth phase in the one-dimensional discrete Gaussian model with 1/(−j)2 interaction at inverse temperature β>1

We consider the one-dimensional discrete Gaussian model with interaction energyg satisfyingg(i, j)=g(i–j)1/(i– j)² and prove that for the inverse temperature>1 this system displays a smooth phase characterized by <(n _{n 0} –n _{y 0})²> C < if the nearest neighbor coupling g(1) is sufficiently large. Our method also allows us to treat the 1/(i– j)² Ising model and reproves the existence of spontaneous magnetization under the above conditions.     

Magnetic penetration depth in V3Si and LiTi2O4 measured by μSR

Muon spin relaxation (SR) studies have been performed in the normal spinel LiTi₂O₄ and the A-15 superconductor V₃Si to measure the magnetic penetration depth . The relaxation rate(T) 1/² in field-cooled measurements shows a sharp increase belowT _c followed by saturation at low temperatures in both systems. This feature implies an isotropic energy gap without anomalous zeros, and most likelys-wave pairing. The low temperature penetration depth (T 0) is determined to be 2100Å for LiTi₂O₄ and 1300Å for V₃Si respectively. Assuming a clean limit relation ^–2 n _s /m ^*, we derive the Fermi temperatureT _F n _s/ ^2/3 m ^* from the relaxation rate and the Sommerfeld constant asT _F ^3/4–1/4. Unlike conventional superconductors, both LiTi₂O₄ and V₃Si have a large ratio ofT _c /T _F 0.01, only slightly smaller than those ratios in more exotic superconductors.We thank C. Ballard and K. Hoyle for technical assistance. Work at Columbia University is supported by NSF Grant No. DMR-89-13784 and Packard Foundation (YJU). Ames Laboratory is operated for the U. S. Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. Work at Ames was supported by the Director for Energy Research, Office of Basic Energy Sciences.     

Matrix field theory for disordered local pairing superconductors with two glass order parameters and spin-flip pairbreaking processes

We derive the exact matrix field theory for a replicated grassmannian representation of a local pairing superconducting disorder ensemble including three superconducting order parameters and the spin-flip pairbreaking mechanism. Disorder is assumed to be gaussian distributed. We find by exactly solving the saddle-point equation the criterion for a vanishing gap ^–1 + ^–1 , where denotes the averaged superconducting order parameter, ^–1 the spin-flip scattering rate, and ^–1 the scattering rate corresponding to correlations of Re(–). Taken at =0, our field theory, which is exact in all orders of ^–1 , contains new terms in addition to those of theO( ^–1 ) model derived by Efetov et al. Our formulation transfers correctly to all orders the invariances of the action into symmetries of the matrix field theory. The saddle point approximation is outlined and it is shown how singular corrections to the saddle point density of states arise atE _F in a gapless superconductor. Finally singular corrections in the two particle propagator, the density correlation function and the conductivity are calculated for =0 in one loop order. It turns out that these corrections can be entirely expressed by those of the single particle density of states.     

Note on the interfacial tension of phase-separated polymer solutions

Earlier theoretical calculations of the interfacial tension of phase-separated polymer solutions as a function of the degree of polymerizationN and the temperatureT, based partly on the mean-field approximation, had led toN ^–1/4(1–T/T _c )^3/2 for fixedN1 andT approaching the critical solution temperatureT _c It is here remarked that the scaling procedure of de Gennes then modifies this toN ^–0.37(1–T/T _c )^1.26, which is in close accord with the experimentalN ^–0.44(1–T/T _c )^1.26. The simplest mean-field picture yieldsN ^–1/2(1–T/T _c )^3/2.     

Attractor States and Quantum Instabilities in de Sitter Space

The asymptotic behavior of the energy–momentum tensor for a free quantized scalar field with mass m and curvature coupling in de Sitter space is investigated. It is shown that for an arbitrary, homogeneous, and isotropic, fourth-order adiabatic state for which the two-point function is infrared finite, T _ab approaches the Bunch–Davies de Sitter invariant value at late times if m ² + R > 0. In the case m = = 0, the energy–momentum tensor approaches the de Sitter invariant Allen–Folacci value for such a state. For m ² + R = 0 but m and not separately zero, it is shown that at late times T _ab grows linearly in terms of cosmic time leading to an instability of de Sitter space. The asymptotic behavior is again independent of the state of the field. For m ² + R < 0, it is shown that, for most values of m and , T _ab grows exponentially in terms of cosmic time at late times in a state dependent manner.     

Glueball spectroscopy in strongly coupled lattice gauge theories

We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action (g _P) for real irreducible and small . Besides the lowest excitationm ₀–4log, we find two nearly degenerate excited statesm ₁,m ₂ withm _i–6log (i=1, 2) and (m ₁–m ₂) at leastO().Work partially supported by CNPq (Brasil)     

Dynamics of vector spin glasses: The Gabay-Toulouse line

The dynamics of ann-component vector spin glass with infinite range interactions are investigated near and above the Gabay-Toulouse (GT) line. The local transverse susceptibility _T for 0 varies along the whole GT lineT _c1 (H) as ^v , with a field and temperature independent critical exponentv=1/2. The longitudinal susceptibility _L () remains analytic for all (T, H)T _c1 (H), except for a cross-over fromv=1 tov=1/2 forH0 at the freezing temperatureT=T _f . The dynamic susceptibilities _T () and _L () are already coupled above the GT line via self-energy terms. BelowT _c1 (H), this coupling is strongly enhanced by other mechanisms.     

The 1/D expansion for classical magnets: Low-dimensional models with magnetic field

The field-dependent magnetizationm(H, T) of one- and two-dimensional classical magnets described by theD-component vector model is calculated analytically in the whole range of temperature and magnetic fields with the help of the 1/D expansion. In the first order in 1/D the theory reproduces with a good accuracy the temperature dependence of the zero-field susceptibility of antiferromagnets with maximum atT|J ₀|/D (J ₀ is the Fourier component of the exchange interaction) and describes for the first time the singular behavior of (H, T) at small temperatures and magnetic fields: lim _T0 lim _H0 (H, T)=1/(2|J ₀|)(1–1/D) and lim _H0 lim _T0 (H, T)=1/(2|J ₀|).     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

Magnetic behaviour ofCuAuFe alloys

The magnetic properties of Cu_99-xAu_xFe₁ alloys (x=12, 37 and 50.7 ats) have been investigated over the temperature range 4.2–70 K using low field AC magnetic susceptibility measurements and mössbauer spectroscopy. All alloys exhibit spin glass behaviour at low temperature with freezing temperatures T_f-5.7–7.6 K. Results of analysis of the high temperature (T3 T_f) Curie-Weiss behaviour are compared with those obtained from analysis of the broadly distributed 4.2 K Mössbauer spectra.     

Dependence of the magnetic susceptibility of the palladium silver alloy system on temperature and composition

Starting from thermodynamic considerations an analytical expression (T, x) is given for the variation of the magnetic susceptibility of the substitutional Pd_1–x Ag _x alloy series with both temperatureT and fractional silver contentx. The observed rapid decrease of the isothermal susceptibility (T=const,x) with increasingx and the disappearance of the maximum of the low temperature isopleths (T,x=const) forx0.1 can be specified by three fitting constants related to microscopic model parameters.     

New phenomena in homoepitaxial growth of metals

The growth of Pt(111) by Pt vapour deposition is studied by He diffraction as a function of substrate temperature and deposition rate. At a deposition rate of about 2.5×10^–2 monolayers/second several growth modes are observed: layer-by-layer (2D-) growth at 450 KT _s800 K, multilayer (3D-) growth at 340 KT _s450 K and reentrant layer-by-layer (2D-) growth at T _s340 K. The observed growth modes and in particular the reentrant 2D-growth are shown to be characteristic of growing Pt(111) under clean conditions, i.e. not influenced by contaminants. The influence of the intra- and interlayer mass transport on the growth mode is discussed in the light of experimental and simulation results. The 3D-growth mode is attributed to the existence of an activation barrier which suppresses the descent of adatoms from the top of the growing adatom islands onto the lower terraces. The barrier can be overcome by thermal adatoms at T _s450 K enabling interlayer mass transport which leads to 2D-growth. The reentrant 2D-growth occurs due to a break down of this barrier for small, irregularly shaped islands.     

Free energy and singularity of ferroelectric BixSb1−xSI solid-solution semiconductors

The temperature dependences of the permittivity () and spontaneous polarization (P_s) measured at high pressures for Bi_xSb_1–xSI crystals were used to calculate the coefficients (,,) of the thermodynamic expansion and to plot the dependences of the free energy on the polarization [ F(P_s) ] for various values of p and x. An, analysis was made of the influence of pressure and isomorphous substitution of the components on the nature of phase transitions in Bi_xSb_1–xSI solid solutions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 29–33, November, 1980.     

On the relaxation time of Gauss' continued-fraction map. II. The Banach space approach (transfer operator method)

The spectrum of the transfer operator for the mapTx=1/x–[1/x] when restricted to a certain Banach space of holomorphic functions is shown to coincide with the spectrum of the adjointU* of Koopman's isometric operatorUf(x)=f·T(x) when the former is restricted to the Hilbert space () introduced in part I of this work. IfN denotes the operator –P ₁ withP ₁ the projector onto the eigenfunction to the dominant eigenvalue ₁ =1 of , then –N is au ₀-positive operator with respect to some cone and therefore has a dominant positive, simple eigenvalue – ₂. A minimax principle holds giving rigorous upper and lower bounds both for ₂ and the relaxation time of the mapT.     

Damage spreading in a single-component irreversible reaction process: Dependence of the system's immunity on the Euclidean dimension

The spreading of a globally distributed damage, created in the stationary regime, is studied in a single-component irreversible reaction process, i.e., the BK model [Browne and Kleban,Phys. Rev. A 40, 1615 (1989)]. The BK model describes one variant of the A+AA₂ reaction process on a lattice in contact with a reservoir of A species. The BK model has a single parameter, namely the rate of arrival of A species to the lattice (Y). The model, exhibits an irreversible phase transition between a stationary reactive state with production of A₂ species and a poisoned state with the lattice fully covered by A species. The transition takes place at critical points (Y _C ) which solely depend on the Euclidean dimensiond. It is found that the system is immune ford=1 andd=2, in the sense that even 100% of initial damage is healed within a finite healing period (T _H ). Within the reactive regime,T _H diverges when approachingY _C according toT _H (Y _C –Y)^–, with 1.62 and 1.08 ford=1 andd=2, respectively. Ford=3 a frozen-chaotic transition is found close toY _s 0.4125, i.e., well inside the reactive regime 0YY _C 0.4985. Just atY _S the damageD(t) heals according toD(t) t ^–, with 0.71. For the frozen-chaotic transition atd=3 the order parameter critical exponent 0.997 is determined.