The spectral moments method

Benoît, C.; Royer, Emmanuel; Poussigue, G.

doi:10.1088/0953-8984/4/12/010

Cited by 96 publications

(94 citation statements)

References 28 publications

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“…For each LJ-like potential, two sets of glasses were prepared: one had N =2000 atoms and its dynamical matrix was diagonalized, while the other, 10000 atoms, was used for the calculation of S(Q, ω) by the method of moments [12]. The bond percolators had dimension 80 3 and two bond concentrations, 0.45 and 0.65 respectively, the spring-disordered lattices had dimension 80 3 ; for both S(Q, ω) was calculated by the method of moments.…”

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confidence: 99%

Frustration and Sound Attenuation in Structural Glasses

et al. 2000

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Three classes of harmonic disorder systems (Lennard-Jones like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the mechanism of high frequency sound attenuation. We introduce the concept of frustration in structural glasses as a measure of the internal stress, and find a strong correlation between the degree of frustration and the exponent α that characterizes the momentum dependence of the sound attenuation Γ(Q)≃Q α . In particular, α decreases from ≈d+1 in lowfrustration systems (where d is the spectral dimension), to ≈2 for high frustration systems like the realistic glasses examined.PACS numbers: 63.50.+x, 61.43.Fs The nature of collective excitations in disordered solids has been one of the major problems of condensed matter physics during the last decades; the recent devolopment of a high-resolution inelastic X-ray scattering (IXS) facility [1] made Brillouin-like experiments possible in the region of mesoscopic exchanged momenta Q=1÷10 nm −1 , which led to the realization that propagating sound-like excitations exist in glasses up to the Terahertz frequency region. The quantity that characterizes the collective excitations, and which has been determined experimentally in many glasses [2] and liquids [3], is the dynamic structure factor S(Q, ω). Although specific quantitative differences exist among systems, the following qualitative characteristics are common to all the investigated materials: i) there exist propagating acoustic-like excitations for Q values up to Q m , with Q m /Q o ≈0.1÷0.5 (where Q o is the position of the maximum in the static structure factor), which show up as more-or-less well defined Brillouin peaks at Ω(Q) in S(Q, ω), the specific value of Q m /Q o is correlated with the fragility of the glass; ii) the slope of the (almost) linear Ω(Q) vs Q dispersion relation in the Q→0 limit extrapolates to the macroscopic sound velocity; iii) the width of the Brillouin peaks, Γ(Q), follows a power law, Γ(Q)=DQ α , with α≈2 whithin the statistical uncertainties; iv) the value of D does not depend significantly on temperature, indicating that the broadening (i.e. the sound attenuation) in the high frequency region does not have a dynamic origin, but that it is due to disorder [4]. These general features of S(Q, ω) have been confirmed by numerical calculations on simulated glasses [5], obtained within the framework of the mode coupling theory [6], and, more recently, ascribed to a relaxation process associated to the topological disorder [7]. However, except for the simple 1-dimensional case [8], the widespread finding Γ(Q)=DQ 2 , has not yet been explained on a microscopic basis.To this end in this Letter we investigate, in the harmonic approximation, systems showing disorder of different characteristics, and the role played by the latter in determining the value of the exponent α. The analyzed systems show either substitutional (bond percolators and spring disordered syst...

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confidence: 99%

Frustration and Sound Attenuation in Structural Glasses

et al. 2000

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“…͑4͒ requires the average of the density of states ͓see Eq. ͑2͔͒ on spin configurations straightforwardly generated according to the Boltzmann weight associated to the Hamiltonian H 0 and temperature T. The key point is that g(E;͕S͖) can be numerically calculated on very large lattices without further approximations using the method of moments 33 ͑complemented with a standard truncation procedure 34 ͒. We have extracted the spin-averaged density of states on a 64ϫ64ϫ64 lattice ͑for these sizes, we estimate that finite-size effects are negligible͒.…”

Section: Methodsmentioning

confidence: 99%

Discontinuous transitions in double-exchange materials

et al. 2001

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It is shown that the double-exchange Hamiltonian, with weak antiferromagnetic interactions, has a rich variety of first-order transitions between phases with different electronic densities and/or magnetizations. The paramagnetic-ferromagnetic transition moves towards lower temperatures, and becomes discontinuous as the relative strength of the double-exchange mechanism and antiferromagnetic coupling is changed. This trend is consistent with the observed differences between compounds with the same nominal doping, such as La 2/3 Sr 1/3 MnO 3 and La 2/3 Ca 1/3 MnO 3 . Our results suggest that, in the low doping regime, a simple magnetic mechanism suffices to explain the main features of the phase diagram.

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“…On the other hand, since in real systems the lower energy glassons have been claimed [23,29] to have transverse polarization, in this work we shall support the universal character of the transition by extending the Euclidean Random Matrix Theory to a generic model with longitudinal and transverse modes. Our aim is to check the validity of the predictions of the vectorial ERM computation on a simple Gaussian model whose spectral properties have been numerically studied by the method of moments [32]. As a matter of fact the theory predicts that the behaviour of some of the main spectral features, namely the arising of the BP and the broadening of the Brillouin peak, are universal and hence can be captured even by the simplest model.…”

Section: Introductionmentioning

confidence: 99%

Brillouin and boson peaks in glasses from vector Euclidean random matrix theory

Ciliberti

Grigera

Martı́n-Mayor

et al. 2003

The Journal of Chemical Physics

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A simple model of harmonic vibrations in topologically disordered systems, such as glasses and supercooled liquids, is studied analytically by extending Euclidean Random Matrix Theory to include vector vibrations. Rather generally, it is found that i) the dynamic structure factor shows sound-like Brillouin peaks whose longitudinal/transverse character can only be distinguished for small transferred momentum, p, ii) the model presents a mechanical instability transition at small densities, for which scaling laws are analytically predicted and confirmed numerically, iii) the Brillouin peaks persist deep into the unstable phase, the phase transition being noticeable mostly in their linewidth, iv) the Brillouin linewidth scales like p 2 in the stable phase, and like p in the unstable one. The analytical results are checked numerically for a simple potential. The main features of glassy vibrations previously deduced from scalar ERMT are not substantially altered by these new results.

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The spectral moments method

Cited by 96 publications

References 28 publications

Frustration and Sound Attenuation in Structural Glasses

Frustration and Sound Attenuation in Structural Glasses

Discontinuous transitions in double-exchange materials

Brillouin and boson peaks in glasses from vector Euclidean random matrix theory

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