Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

Monte Carlo calculations of angular momentum projected many-body matrix elements in the Pairing Plus Quadrupole Model

We extend the recently presented formalism for Monte Carlo calculations of the partition function, for both even and odd particle number systems (Phys. Rev. C 59, 2500 (1999)), to the calculation of many-body matrix elements of the type <ψ| e ^{- βℋ}|ψ> where |ψ> is a many-body state with a definite angular momentum, parity, neutron and proton numbers. For large β such matrix elements are dominated by the lowest eigenstate of the many-body Hamiltonian ℋ, corresponding with a given angular momentum parity and particle number. Emphasis is placed on odd-mass nuclei. Negligible sign fluctuations in the Monte Carlo calculation are found provided the neutron and proton chemical potentials are properly adjusted. The formalism is applied to the J ^π = 0⁺ state in ¹⁶⁶ Er and to the J ^π = 9/2^-, 13/2⁺, 5/2^- states in ¹⁶⁵ Er using the pairing-plus-quadrupole model. Received: 28 April 2000 / Accepted: 20 September 2000     

Determination of nonlinear σ-ω-ρ model parameters in the relativistic mean-field theory by nuclear-matter properties

The parameters of the σ-ω-ρ model in the relativistic mean-field theory with nonlinear σ-meson self-interaction are determined by nuclear-matter properties, which are taken as those extracted by fits to data based on nonrelativistic nuclear models. The values of the relevant parameters are C _σ ²∼ 94, C _ω ²∼ 32, C _ρ ²∼ 26, b∼ - 0.09, c∼ 1, and the σ-meson mass m _σ∼ 370 MeV, while the value of the calculated nuclear- surface thickness is t∼ 1.4 fm. The field system is shown to be stable, since the σ-meson self-interaction energy is a lower bound in this whole parameter region with positive c. On the other hand, the effective nucleon mass M^* is larger than 0.73M, if the symmetry incompressibility K_s is assumed to be negative and the nuclear-matter incompressibility K₀ is kept less than 300 MeV. Received: 27 June 2001 / Accepted: 5 October 2001     

Interactions of charmed mesons with nucleons in the ¯<Emphasis Type="Italic">p</Emphasis><Emphasis Type="Italic">d</Emphasis> reaction

We study the possibility to measure the elastic ΦN (Φ≡J/ψ,ψ(2S), ψ(3770), χ_2c) scattering cross section in the reaction ˉp+d→Φ+n _sp and the elastic D(ˉD)N scattering cross section in the reaction ˉp+d→D ⁻ D ⁰ p _sp. Our studies indicate that the elastic scattering cross sections can be determined for Φ momenta about 4–6 GeV/c and D/ˉD momenta 2–5 GeV/c by selecting events with p _t≥ 0.4 GeV/c for Φ's and p _t(p _sp) ≥ 0.5 GeV/c for D/ˉD-meson production. Received: 8 November 1999     

A fractional-spin phase in the power-law Kondo model

We consider a Kondo impurity coupled to a fermionic host with a power-law density of states near the Fermi level, ρ(ε) ∼ |ε|^r, with exponent r < 0. Using both perturbative renormalization group (poor man's scaling) and numerical renormalization group methods, we analyze the phase diagram of this model for ferromagnetic and antiferromagnetic Kondo coupling. Both sectors display non-trivial behavior with several stable phases separated by continuous transitions. In particular, on the ferromagnetic side there is a stable intermediate-coupling fixed point with universal properties corresponding to a fractional ground-state spin. Received 18 February 2002 Published online 31 July 2002     

Field-theoretical Renormalization-Group approach to critical dynamics of crosslinked polymer blends

We consider a crosslinked polymer blend that may undergo a microphase separation. When the temperature is changed from an initial value towards a final one very close to the spinodal point, the mixture is out equilibrium. The aim is the study of dynamics at a given time t, before the system reaches its final equilibrium state. The dynamics is investigated through the structure factor, S(q, t), which is a function of the wave vector q, temperature T, time t, and reticulation dose D. To determine the phase behavior of this dynamic structure factor, we start from a generalized Langevin equation (model C) solved by the time composition fluctuation. Beside the standard de Gennes Hamiltonian, this equation incorporates a Gaussian local noise, ζ. First, by averaging over ζ, we get an effective Hamiltonian. Second, we renormalize this dynamic field theory and write a Renormalization-Group equation for the dynamic structure factor. Third, solving this equation yields the behavior of S(q, t), in space of relevant parameters. As result, S(q, t) depends on three kinds of lengths, which are the wavelength q ⁻¹, a time length scale R(t) ∼ t ^1/z , and the mesh size ξ ^*. The scale R(t) is interpreted as the size of growing microdomains at time t. When R(t) becomes of the order of ξ ^*, the dynamics is stopped. The final time, t ^*, then scales as t ^* ∼ ξ ^{* z}, with the dynamic exponent z = 6−η. Here, η is the usual Ising critical exponent. Since the final size of microdomains ξ ^* is very small (few nanometers), the dynamics is of short time. Finally, all these results we obtained from renormalization theory are compared to those we stated in some recent work using a scaling argument.     

Two-point correlation function in systems with van der Waals type interaction

The behavior of the bulk two-point correlation function G(;T| d ) in d-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such finite systems with periodic boundary conditions is discussed within mean-spherical model which is an example of Ornstein and Zernike type theory. The interaction is supposed to decay at large distances r as r ^{- (d + σ)}, with 2 < d < 4, 2 < σ < 4 and d + σ≤6. It is shown that G(;T| d ) decays as r ^{- (d - 2)} for 1 ≪r≪ξ, exponentially for ξ≪r≪r ^*, where r ^* = (σ - 2)ξlnξ, and again in a power law as r ^{- (d + σ)} for r≫r ^*. The analytical form of the leading-order scaling function of G(;T| d ) in any of these regimes is derived. Received 28 May 2001     

The reaction pp→pΛK + near threshold

We analyze the recent total cross section data for pp→pΛK ⁺ near threshold measured at COSY. Using an effective range approximation for the on-shell pΛ S-wave final state interaction we extract from these data the combination ?= (2|K _s|²+|K _t|²)^−1/2= 0.38 fm⁴ of the singlet (K _s) and triplet (K _t) threshold transition amplitudes. We present an exploratory calculation of various (tree-level) vector and pseudoscalar meson exchange diagrams. Pointlike ω-exchange alone and the combined (ρ⁰,ω,K^*+)-exchange can explain the experimental value of ?. The pseudoscalar meson exchanges based on a SU(3) chiral Lagrangian turn out to be too large. However, when adding π⁰-exchange in combination with the resonant πN→S ₁₁(1650) →KΛ transition and introducing monopole form factors with a cut-off Λ_c= 1.5 GeV one is again able to reproduce the experimental value of ?. More exclusive measurements are necessary to reveal the details of the pp→pΛK ⁺ production mechanism. Received: 28 October 1998 / Revised version: 12 January 1999     

Hadron diffractive processes: the structure of soft pomeron and colour screening

On the basis of the experimental data on diffractive processes in πp, pp and pˉp collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality of cross sections such as σ^tot _πp/σ^tot _pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion and proton (antiproton) in the impact parameter space of quarks, σ_π(r _1⊥, r _2⊥; s) and σ_p(r _1⊥, r _2⊥, r _3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r _i⊥−r _k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented. Received: 15 December 1998     

Heat capacity of MnBr2·4H2O near the antiferromagnetic transition temperature

Heat capacity of MnBr₂·4H₂O has been measured in the critical region around the Neel temperature. The data can be fitted, over a restricted range of |t|⩽10⁻², to the asymptotic power law. The critical exponents and the amplitudesA andA′ are not consistent with any theoretic predictions. However when scaling constraints are imposed, their values agree with the parameters of Ising model. Corrections to scaling are necessary to extend the range of the fit to |t|>10⁻². The correction terms are asymmetric giving −1·15±0·25 as the ratio of the amplitudes of the lowest order correction terms,D andD′ above and belowT _c. This value is in agreement with the recent predictions of the renormalisation group theory.     

On the envelope soliton near critical density in a plasma with cold ions and two-temperature electrons

Summary We have analysed the formation of envelope soliton near critical density in a plasma consisting of two-temperature electrons and cold ions. The non-linear Schr?dinger-like equation obtained isiφ _t +pφ _xx +q|φ|⁴φ=0 which we call the modified non-linear Schr?dinger equation. It is also observed that this approach leads to a physical situation where a linear combination of both the modified and usual NLS equations holds, in the formiφ _t +pφ _xx +q ₁|φ|²φ +q ₂|φ|⁴φ=0. It is demonstrated through graphical analysis thatq ₁,q ₂, thought of as a function of β(=T _el/T _eh), behave in opposite way. That is, whenq ₁ grows,q ₂ decays, or vice versa. Lastly we demonstrate that this equation can sustain a type of solution other than the usual solitary profile. The form of such a wave is also depicted graphically.     

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to instabilities with mound formation whose typical linear size L increases with time (coarsening process). In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening is known to be logarithmic in the absence of noise ( L(t) ∼ ln t) and to follow a power law ( L(t) ∼t ^1/3) when noise is present. If the surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stages of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster : if α is the exponent describing the steepening of the maximal slope M of mounds ( M ^α∼L) we find that L(t) ∼t ⁿ: n is equal to for 1≤α≤2 and it decreases from to for α≥2, according to n = α/(5α - 2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t) ∼t ^1/4, irrespectively of α. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model α = 1, both in the absence and in the presence of noise. Received 28 September 2001 and Received in final form 21 November 2001     

The K * Kπ and ρππ couplings in QCD

The light cone QCD sum rules are derived for the K ^* Kπ coupling g _K ^* Kπ and the ρππ coupling g _ρππ. The contribution from the excited states and the continuum is subtracted cleanly through the double Borel transform with respect to the two external momenta, p ₁ ², p ₂ ²= (p−q)². Our result g _K ^* Kπ= (8.7 ± 0.5) and g _ρππ= (11.5 ± 0.8) is in good agreement with the experimental value. Received: 31 July 1998 / Revised version: 20 November 1998     

Commensurate-incommensurate transition in two-coupled chains of nearly half-filled electrons

We investigate the physical properties of two coupled chains of electrons, with a nearly half-filled band, as a function of the interchain hopping t _⊥ and the doping. We show that upon doping, the system undergoes a metal-insulator transition well described by a commensurate-incommensurate transition. By using bosonization and renormalization we determine the full phase diagram of the system, and the physical quantities such as the charge gap. In the commensurate phase two different regions, for which the interchain hopping is relevant and irrelevant exist, leading to a confinement-deconfinement crossover in this phase. A minimum of the charge gap is observed for values of t _⊥ close to this crossover. At large t _⊥ the region of the commensurate phase is enhanced, compared to a single chain. At the metal-insulator transition the Luttinger parameter takes the universal value K _ρ ^* = 1, in agreement with previous results on special limits of this model. Received 31 July 2000     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Lifetimes of triaxial superdeformed states in 163Lu and 164Lu

Lifetimes of states in the yrast superdeformed bands of ¹⁶³Lu and ¹⁶⁴Lu were determined in a Doppler-shift attenuation-method experiment. From fractional Doppler shifts and line shapes, average transition quadrupole moments, Q _t = 8.2_-0.6 ^+1.0 b and 7.1_-0.6 ^+0.5 b, were deduced for one of the bands in ¹⁶³Lu and ¹⁶⁴Lu, respectively. These values are much larger than the quadrupole moment of the normal-deformed yrast band in ¹⁶³Yb, Q _t = 4.9_-0.4 ^+1.3 b, that was also determined in this experiment. Comparison to cranking calculations indicates that both superdeformed bands correspond to a local potential energy minimum with a pronounced triaxiality, γ∼ 20^°. Received: 8 November 2001 / Accepted: 9 January 2002     

Impurity effects on the critical behaviour of the electrical resistance of binary liquid mixtures

The electrical resistance of the binary liquid system cyclohexane + acetic anhydride is measured, in the critical region, both in the pure mixture and when the mixture is doped with small amounts (≈ 100 ppm) of H₂O/D₂O impurities.T _c was approached to aboutt=3×10⁻⁶ wheret=(T −T _c )/T _c . The critical exponentb ≈ 0.35 in the fit of the resistance data to the equationdR/dT ∼t ^−b does not seem to be affected appreciably by the impurities. There is a sign reversal ofdR/dt in the non-critical region. Binary liquid systems seem to violate the universality of the critical resistivity.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Triviality of Hierarchical Models with Small Negative φ4 Coupling in Four Dimensions

The Kadanoff-Wilson renormalization group (RG) for a class of hierarchical spin models including small negative φ⁴ terms in four dimensions are studied by using Gawędzki and Kupiainen's analysis. We prove triviality for the class, namely prove existence of critical trajectory that leads to the Gaussian fixed point.