Non-equilibrium structure factor for the disordering of adsorbed monolayers

We consider the non-equilibrium, time-dependent elastic-scattering structure factor S(q,t), for the disordering of an ordered overlayer, initially in equilibrium at temperature T_I and characterized by the structure factor S(q,0)=x(q,T_I, upon a sudden increase in temperature T_I→T_F at constant coverage, such that the adsorbates equilibrate at T_F in a disordered phase. The initial decay of a peak in x(q,T_I) proceeds exponentially in time, $\text{exp}\text{(−}\text{t}\text{τ}{}_{\mathrm{q}}\text{)}$, where τ_q is a wavevector-dependent lifetime, before it crosses over to a power-law, t⁻¹ decay. When x(q,T_I) is peaked at the boundaries of the Brillouin zone (BZ), the peak approximately maintains its shape in q-space as it decays exponentially. Except near the center of the BZ, after the peak has decayed sufficiently, the dependence of S(q,t) on q is as though the spins quasi-equilibrate to the equilibrium structure factor associated with T_F, x(q,T_F), in that the ratio $\text{S(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ is independent of q, is dependent on time, approaching unity as t⁻¹ for large t. For systems exhibiting an initial peak for q ≈ 0, the peak decays exponentially but does not preserve its shape, since τ_q strongly depends on q, diverging as q⁻² for q→0. For these systems too, away from the center of the BZ, $\text{S}\text{(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ rapidly evolves to a slowly decaying function of $\text{t}\text{t}{}_{\mathrm{w}}$, independent of q. In this case, however, the characteristic time scale, t_w, is anomalously long, proportional to ξ², where ξ is the correlation length associated with the initial state. This behavior of t_w can be related to the random walk of domain boundaries.     

Scaling function for order-parameter correlations in expansion to order 1/n: I. Short-range interactions

The order-parameter correlation function $\text{G}\text{?}\text{(}\text{q}\text{, ξ}{}_1\text{)}$ is calculated in the critical region of momentum space $\text{q}$ in terms of a second-moment correlation length ξ₁ by means of perturbation expansion to order 1/n, for an n-vector system with short-range interactions, in zero field above T_c, for 2 < d < 4. The scaling function of the $\text{q}$ dependence is obtained in closed form with a precisely identified cutoff-dependent factor which is the amplitude of the correlation-length dependence of the susceptibility. Both the exponents and the coefficients of the expansion for fixed q as t = (T?T_c)/T_c → 0 are given explicitly and the former are shown to be in accordance with the operator product expansion. The coefficients of order 1/n in the terms associated with a t^k(1?α) dependence of the energy density, for integer k ≥ 1, are expected to be explicitly cutoff-dependent and this is verified by the detailed calculations for k = 1. The behaviour for fixed t and q → 0 is shown to be markedly different from the Ornstein-Zernike approximation. Detailed comparison is provided with the scaling function of the t dependence of the correlations appearing in parallel work.     

Raman study of charge-density-wave phase transition in quasi-one-dimensional conductor (TaSe4)2I

Polarized Raman spectra were obtained in the quasi-one-dimensional conductor (TaSe₄)₂I above and below the charge-density-wave (CDW) transition temperature (T_c=263 K). The Raman intensities of many peaks become intenser and two of the phonon peaks shift to higher frequency with decreasing temperature. Moreover a new broad peak at about 90 cm^?1 and a new peak around 166 cm^?1 appear in the low-temperature phase. The polarization characteristic shows that the former is assigned to totally symmetric mode. The damping constant of the phonon at 90 cm^?1 increases markedly with increasing temperature. The frequency shifts to higher frequency as the temperature increases and the coupling coefficient is approximately proportional to (T_c?T)^{$\text{1}\text{2}$}. This peak becomes Raman active owing to the CDW phase transition. The temperature dependence of the damping constant and the frequency shift may have a relation to the dynamical properties of the CDW phase transition.     

Dynamics of the infinite-range ising spin glass

The Glauber dynamics of an Ising spin glass with infinite-range interactions and additional static field, h, is investigated near the freezing temperature, T_f. We obtain critical slowing down at and below the de Almeida-Thouless instability line, h_c(T), to order (1?T/T_f)³ with algebraic decay of the spin correlations ～t^?ν, where $\text{ν=}\text{1}\text{2}$ at T_f and $\text{ν≤}\text{1}\text{2}$ for T<T_f.     

Paramagnetic resonance study of fluctuations near phase transition in triglycine sulphate

The EPR line widths of the high and the low field resonances of Cr³⁺ in triglycine sulphate (TGS) show two distinct anomalous broadenings near T_c. One is associated with a change in the motional frequency of the hindered rotation of the NH₃ groups and the other is related to the fluctuation of the polarization. Just below T_c there is a two fold splitting of the resonances which has a$\text{(}\text{T}{}_{\mathrm{c}}\text{?}\text{T}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ temperature dependence indicating the local geometry about the Cr³⁺ ion is determined by mean field theory.     

Solving the linearized Φ4 equation in external driving fields

The Φ⁴ equation, linearized about a kink at rest, is solved for external driving fields F(t) = Σ_i=n^∞f_itⁱ. The x-dependent part of the solution $\text{u}\text{?}\text{(x, t)}$ is proportional to the translation mode. This implies that also for large times the kink's dynamics is adiabatic, if the external field is sufficiently weak and $\text{|}\text{u}\text{?}\text{|? z1}$|ν| ? 1.     

Investigation of the central component of SrTiO3 by neutron scattering with eV resolution

We studied the energy width and the width in reciprocal space Δq of the central mode of SrTiO₃ above T_c. At T_c+4° we observed an energy width of about 6×10^?7 eV. If the measured Δq is interpreted by a correlation length $\text{Δq}{}^{\mathrm{?1}}\text{= ξ = ξ}{}_0\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>2</mtext><mtext>3</mtext>}}$ we obtain $\text{ξ}{}_0\text{= 75}\text{A}\text{?}$.     

The pair distributions and the osmotic coefficient in anomalous electrolytes up to concentrations c≈ 1 mol/1

The osmotic coefficient of anomalous electrolytes up to concentrations c ≈ 1 mol/l is explained by the pair distributions $\text{n(r) =}\text{exp}\text{[-β(}\text{V}{}_{\mathrm{c}}\text{(r) + V(}{}^{\mathrm{hs}}\text{)(r) + V}{}_1\text{(r))]}$. Here $\text{V}$_c(r) is a screened Coulomb potential, V(^hs)(r) a hard sphere potential and V₁(r) = ?A/r⁶ a short range attractive potential. For the contact distances R₊₊, R_?? and R_+? of the hard sphere potentials between ions with the same sign of their charges (++,??) and ions of opposite charges (+?) the relations R₊₊ = R_?? = R and R_+? = q₁R with 0 < q₁ < 1 are assumed. In contrast to a previous paper the parameter q₁ takes a fixed value q₁ ≈ 0,8. The constant A is determined by the fraction q₂ defined by A/R⁶ = q₂(Z²e²/DR) where the positive integer Z is the charge number of the ions and D the dielectric constant of the solvent. The numerical calculation of the osmotic coefficient of 1-1-valent hydrous electrolytes in the range of temperature 273 K ? T ? 293 K shows that the anomalous electrolytes are described by fractions q₂ in the range 0,25 ? q₂ ? 0,5 if the contact distances R are in the range $\text{3}\text{A}\text{?}\text{? R ? 7}\text{A}\text{?}$.     

Flow birefringence in critical fluids

Flow birefringence is examined in classical fluids near the critical point under oscillating incompressible flows. This effect originates from anisotropy in the fluctuation part of the dielectric tensor in the presence of a flow and is found to be enhanced near the critical point. When the flow is stationary, the birefringence phase shift δ is proportional to ξ²D in the weak shear regime and to $\text{D}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ in the strong shear regime where ξ is the correlation length and D is the shear rate. For the oscillatory case we examine only the weak shear regime. One characteristic feature is that δ becomes independent of T ? T_c when the frequency of the flow exceeds the average decay rate of critical fluctuations.     

Effect of pressure on the Curie temperature of PdFe,PdCo, PtFe and PtCo alloys

The Curie temperatures of $\text{Pd}$Fe, $\text{Pd}$Co, $\text{Pt}$Fe and $\text{Pt}$Co alloys with Fe or Co concentrations between 1 and 10 at. % have been measured by thermal scanning of the ⁵⁷Fe Mössbauer resonance under pressures up to 170 kbar. Systematically, the largest (positive) values of the logarithmic derivative, dlnT_e/dlnV, are found in the most dilute alloys. The data are compared with models, which relate the variation of T_c under pressure to changes in the impurity spin-conduction electron coupling parameter, J_i, and to changes of the pure host metal susceptibility, χ_h. The discrepancies between the experimental data and these models are discussed.     

Phase transitions in classical vector models

The equation of state obtained earlier /6/ for 3-dimensional Ising ferromagnets in the first order in$\text{1}\text{z}$ (z is the number of the nearest neighbours) is generalized with regard to the classical D-component vector model. The results obtained are valid in a wide temperature range |τ|?[z²(D+2)]^?1 (τ=(T_c-T)/T_c) and become exact in the limit D → ∞.     

The impurity resistivity and resistivity minima in AlCr and AlMn alloys

The impurity resistivity of $\text{Al}$Cr between 1.5 and 50°K was determined with a characteristic temperature for the T² variation θ₁=960±40°K. The behaviour of the resistivity minimum both in $\text{Al}$Cr and $\text{Al}$Mn alloys with impurity concentration provides evidence that a T³ phonon resistivity is found also in aluminium with anomalous impurity resistivity.     

Variational principle for t-dependent classical Hamiltonian systems

For a non-conservative, classical system described by Lagrangian L(q?, q_i, t), the functional $\text{Z = ?}{}^{\mathrm{T}}{}_0\text{L}\text{d}\text{t + KT}$, where K is constant, is stationary with respect to variations in q_i(t) and T, given suitable boundary conditions. In the conservative case, for systems with a single periodic coordinate, this variational procedure reduces to that given by Luttinger and Thomas.     

Critical dynamics in isotropic ferromagnets

Modern high resolution inelastic neutron scattering methods make very long wavelength fluctuations accessible to dynamical investigation. The new results on Fe and EuO show that: (a) the $\text{q}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ power law is well borne out at T = T_c; (b) strong zero-wavenumber relaxation due to spin non-conserving forces can make the predicted hydrodynamic spin diffusion at T >T_c unobservable; (c) this zero-wavenumber relaxation is the only appreciable deviation from the $\text{z =}\text{5}\text{2}$ exchange scaling behaviour; (d) there is no evidence for the predicted cross-over to dipolar dynamics a finite q's.     

Conductivity of a quasi-one-dimensional metal at finite temperatures

The longitudinal conductivity of a quasi-one-dimensional metal is calculated for the case T?ω_D (ω_D being the limiting phonon frequency) and ω_Dl¹/v?1 where l¹ is the effective mean free path determined by impurity and phonon scattering: $\text{l}{}^1\text{= (l}{}^{\mathrm{?1}}{}_{\mathrm{ph}}\text{+ l}{}^{\mathrm{?1}}{}_{\mathrm{i}}\text{)}{}^{\mathrm{?1}}\text{, l}{}_{\mathrm{ph}}\text{= v/λT, l}{}_{\mathrm{i}}$ is the impurity mean free path. The conductivity is σ = (c₁e²/πS)l³_iv^?2ω_DλT for l_i?l_ph, σ = (c₂e²/πS)vω_D(λT)^?2 for l_i?l_ph, λ being the dimensionless electron-phonon interaction constant, c₁, c₂ ～ 1, S = a_xa_y is the (xy) area per one chain.     

D and D meson production near 4 GeV in e+e− annihilation

We have studied momentum spectra for D⁰ ($\text{D}$⁰) and D^± mesons produced near 4 GeV in e⁺e^? annihilation and find that production is dominated by two-body reactions involving D and D¹ states where the D¹ (charged and neutral) have masses near 2.01 GeV/c². A detailed study of D momentum spectra near E_cm = 4.028 GeV allows determination of masses and branching ratios of D and D¹ states. Lastly we find that events containing a D⁰ meson conserve strangeness, thus establishing upper limits on D⁰-$\text{D}$⁰ mixing and on the effects of charm changing neutral currents.     

The four-pion final state in pp annihilations at 5.7 GeV/c

577 events from $\text{p}\text{p}\text{→2π}{}^{\mathrm{+}}\text{2π}{}^{\mathrm{?}}$ annihilations at 5.7 GeV/c are analyzed. Single-particle spectra are studied and an effective matrix element in the form Π_i=1⁴ exp(?Bp_Ti²) is determined. The rates for production of ?° and f⁰ mesons are estimated and the influence of resonances on the angular distributions of pions and dipions is investigated. Transverse momenta correlations can be explained using peripheral phase space.     

Dependence on interatomic distance of exchange coupling in rare-earth Al2 compounds

The effect of pressure on the Curie temperature of the heavy rare-earth dialuminides has been measured up to 3.5 kbar. The derivatives dT_c/d_p are 0.00(4), 0.09, 0.21, 0.39, 0.60 and 0.71 K/kbar respectively for TmAl₂ ErAl₂, HoAl₂, DyAl₂, TbAl₂ and GdAl₂ thus indicating a clear positive correlation between dT_c/dp and the de Gennes factor G. The results are discussed in terms of the RKKY model. However, the phenomenological parameter D/d, where D is the nearest-neighbour R-R distance and d the diameter of the 4f orbital, is used to reflect the non-δ-function character of the sf-coupling parameter Г. The experimental values of Г²D² and T_p/G are found to decrease linearly with increasing D/d. This is in keeping with the RKKY proportionality of $\text{T}{}_{\mathrm{c}}\text{?T}{}_{\mathrm{p}}$ to Γ²E^?1_FG. For GdAl₂, TbAl₂ and DyAl₂ the quantity $\text{?}\text{(}\text{d}\text{T}{}_{\mathrm{c}}\text{d}\text{p}\text{)}\text{k}{}_{\mathrm{l}}\text{(}\text{D}\text{d}\text{)}\text{G}$ coincides within the error limits with the slope of the T_p/G vs D/d plot.     

Functional derivative δTc/δα2 (Ω)F(Ω) for weak coupling superconductors

We present approximate analytic calculation of the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω)}$, where T_c is the superconducting critical temperature and $\text{α}{}^2\text{(Ω)F(Ω)}$ is the electron-phonon spectral function, within the “square-well model” for the phonon mediated electron-electron interaction and weak coupling limit $\text{ω}{}_{\mathrm{D}}\text{(2πT}{}_{\mathrm{c}}\text{)? 1 (ω}{}_{\mathrm{D}}$ is the Debye energy). It is found that $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω) = (1 + λ)}{}^{-1}\text{G(Ω)}$ where λ is the familiar electron-phonon coupling parameter and $\text{G(Ω)}$ is a universal function of the reduced frequency $\text{Ω}\text{=}\text{Ω}\text{T}{}_{\mathrm{c}}$. We compare this formula with accurate numerical results for several weak coupling superconductors. The overall agreement is good