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Journal ArticleDOI

Disordered elastic systems and one-dimensional interfaces

TL;DR: In this paper, the authors introduce the generic framework of disordered elastic systems (DES), giving a short "recipe" of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of such systems.
Abstract: We briefly introduce the generic framework of disordered elastic systems (DES), giving a short ‘recipe’ of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of such systems. We then focus on a particular low-dimensional DES, namely the one-dimensional interface in short-ranged elasticity and short-ranged quenched disorder. Illustrating different elements given in the introductory sections, we discuss specifically the consequences of the interplay between a finite temperature T > 0 and a finite interface width ξ > 0 on the static geometrical fluctuations at different lengthscales, and the implications on the quasistatic dynamics.

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Citations
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Journal ArticleDOI
TL;DR: In this article, the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length are studied. But the roughness of the interface, defined as the variance of its endpoint fluctuations, follows a power-law behaviour whose exponent characterises its superdiffusive behaviour.
Abstract: We study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical fluctuations as a function of its length. At large lengthscales, the roughness of the interface, defined as the variance of its endpoint fluctuations, follows a power-law behaviour whose exponent characterises its superdiffusive behaviour. In 1+1 dimensions, the roughness exponent is known to be the characteristic 2/3 exponent of the Kardar-Parisi-Zhang (KPZ) universality class. An important feature of the model description is that its Flory exponent, obtained by a power counting argument on its Hamiltonian, is equal to 3/5 and thus does not yield the correct KPZ roughness exponent. In this work, we review the available power-counting options, and relate the physical validity of the exponent values that they predict, to the existence (or not) of well-defined optimal trajectories in a large-size or low-temperature asymptotics. We identify the crucial role of the 'cut-off' lengths of the problem (the disorder correlation length and the system size), which one has to carefully follow throughout the scaling analysis. To complement the latter, we device a novel Gaussian Variational Method (GVM) scheme to compute the roughness, taking into account the effect of a large but finite interface length. Interestingly, such a procedure yields the correct KPZ roughness exponent, instead of the Flory exponent usually obtained through the GVM approach for an infinite interface. We explain the physical origin of this improvement of the GVM procedure and discuss possible extensions of this work to other disordered systems.

4 citations

Posted Content
TL;DR: In this paper, a scalar-field model was proposed to characterize the roughness exponents of a stripe domain and a bubble domain under alternating magnetic square field pulses, and it was shown that these domains are subject to area reduction as a function of the number of alternating field cycles.
Abstract: Recent experiments show striking unexpected features when sequences of alternating magnetic square field pulses are applied to ferromagnetic samples: domains show area reduction and domain walls change their geometrical properties. In this work, we use a very simple scalar-field model, in which no physical quantities need to be specified a priori, and which only considers two preferential values for an order parameter, short-range exchange, disorder, and temperature. By proposing a numerical protocol that mimics the experimental one used to observe domains with polar magneto-optic Kerr effect microscopy, we show that domains described by the model are also subject to area reduction under sequential field application. We study two domain geometries common in ferromagnetic films: a bubble and a stripe domain. In both cases, the area reduction as a function of the number of alternating field cycles follows a linear combination of an exponentially decreasing function and a linearly decreasing function, as reported for the experiments. We characterize the domain walls geometry by computing its roughness exponents. The obtained roughness exponents are indistinguishable from the ones observed experimentally, not only under alternating fields but also when the standard protocol to measure velocities is numerically emulated.

3 citations


Cites background from "Disordered elastic systems and one-..."

  • ...At larger scales, disorder plays a key role inducing a different power law-scaling ∼ r [30, 47, 48]....

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DissertationDOI
01 Jan 2014
TL;DR: In this paper, the authors focus on BiFeO3, a multiferroiques a temperature ambiante, affichant ferroelasticite, ferroelectricite, ainsi qu'antiferromagnetisme.
Abstract: Ma these se concentre sur un materiau nomme BiFeO3, l’un des rares multiferroiques a temperature ambiante, affichant ferroelasticite, ferroelectricite, ainsi qu’antiferromagnetisme. Le point de depart de cette recherche repose sur le travail intensif experimental et theorique sur ce materiau, ainsi que sur les progres de la croissance des couches minces qui permettent non seulement le controle au niveau quasi-atomique de la qualite du film, mais aussi de la configuration des domaines ferroelectriques/ferroelastiques. Ce controle nous a permis d’examiner de plus pres des parois de domaines, tant d’un point de vue fondamental avec une approche statistique des interfaces elastiques ancrees, qu’en fonction de leurs nouvelles proprietes fonctionnelles qui pourraient etre utilisee dans des applications futures. De plus, il est aussi possible de fabriquer des heterostructures epitaxiales de couches minces avec des interfaces bien definies, qui pourraient donner lieu a de nouveaux phenomenes physiques.

3 citations


Cites background from "Disordered elastic systems and one-..."

  • ...Therefore, a statistical approach is necessary to incorporate the effects of randomness in a real sample, and is given by the general model of a fluctuating elastic manifold in a disordered medium [19, 87]....

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Journal ArticleDOI
TL;DR: In this article, the mean value of the roughness exponent is analyzed for different magnetic field intensities in the creep regime at room temperature for a Pt/Co/Pt thin film and it is shown that it can be rationalized as an effective value in terms of the known universal values corresponding to the depinning and thermal cases.
Abstract: The creep motion of domain walls driven by external fields in magnetic thin films is described by universal features related to the underlying depinning transition. One key parameter in this description is the roughness exponent characterizing the growth of fluctuations of the domain wall position with its longitudinal length scale. The roughness amplitude, which gives information about the scale of fluctuations, however, has received less attention. Albeit their relevance, experimental reports of the roughness parameters, both exponent and amplitude, are scarce. We report here experimental values of the roughness parameters for different magnetic field intensities in the creep regime at room temperature for a Pt/Co/Pt thin film. The mean value of the roughness exponent is $\ensuremath{\zeta}=0.74$, and we show that it can be rationalized as an effective value in terms of the known universal values corresponding to the depinning and thermal cases. In addition, it is shown that the roughness amplitude presents a significant increase with decreasing field. These results contribute to the description of domain wall motion in disordered magnetic thin systems.

3 citations

Journal ArticleDOI
TL;DR: This work considers three cases of numerically simulated one-dimensional interfaces and shows that sample-to-sample fluctuations are rather large when measuring the roughness exponent, and suggests a minimum of independent interface realizations should be used to guarantee sufficient statistical averaging.
Abstract: Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities. Different methods have been used to extract roughness information from such self-affine structures, and in particular their scaling exponents and associated prefactors. Notably, for an experimental characterization of roughness features, it is of paramount importance to properly assess sample-to-sample fluctuations of roughness parameters. Here, by performing scaling analysis based on displacement correlation functions in real and reciprocal space, we compute statistical properties of the roughness parameters. As an ideal, artifact-free reference case study and particularly targeting finite-size systems, we consider three cases of numerically simulated one-dimensional interfaces: (i) elastic lines under thermal fluctuations and free of disorder, (ii) directed polymers in equilibrium with a disordered energy landscape, and (iii) elastic lines in the critical depinning state when the external applied driving force equals the depinning force set by disorder. Our results show that sample-to-sample fluctuations are rather large when measuring the roughness exponent. These fluctuations are also relevant for roughness amplitudes. Therefore a minimum of independent interface realizations (at least a few tens in our numerical simulations) should be used to guarantee sufficient statistical averaging, an issue often overlooked in experimental reports.

3 citations

References
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Book ChapterDOI

[...]

01 Jan 2012

139,059 citations


"Disordered elastic systems and one-..." refers background in this paper

  • ...the imaging of the imbibition line of a fluid on a disordered substrate [26], of a crack front along an heterogeneous weak plane [27] by ultra-fast CCD camera, or of avalanches in ferromagnetic thin films [5]....

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Journal ArticleDOI
TL;DR: The Ginzburg number as discussed by the authors was introduced to account for thermal and quantum fluctuations and quenched disorder in high-temperature superconductors, leading to interesting effects such as melting of the vortex lattice, the creation of new vortex-liquid phases, and the appearance of macroscopic quantum phenomena.
Abstract: With the high-temperature superconductors a qualitatively new regime in the phenomenology of type-II superconductivity can be accessed. The key elements governing the statistical mechanics and the dynamics of the vortex system are (dynamic) thermal and quantum fluctuations and (static) quenched disorder. The importance of these three sources of disorder can be quantified by the Ginzburg number $Gi=\frac{{(\frac{{T}_{c}}{{H}_{c}^{2}}\ensuremath{\varepsilon}{\ensuremath{\xi}}^{3})}^{2}}{2}$, the quantum resistance $Qu=(\frac{{e}^{2}}{\ensuremath{\hbar}})(\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\varepsilon}\ensuremath{\xi}})$, and the critical current-density ratio $\frac{{j}_{c}}{{j}_{o}}$, with ${j}_{c}$ and ${j}_{o}$ denoting the depinning and depairing current densities, respectively (${\ensuremath{\rho}}_{n}$ is the normal-state resistivity and ${\ensuremath{\varepsilon}}^{2}=\frac{m}{M}l1$ denotes the anisotropy parameter). The material parameters of the oxides conspire to produce a large Ginzburg number $\mathrm{Gi}\ensuremath{\sim}{10}^{\ensuremath{-}2}$ and a large quantum resistance $\mathrm{Qu}\ensuremath{\sim}{10}^{\ensuremath{-}1}$, values which are by orders of magnitude larger than in conventional superconductors, leading to interesting effects such as the melting of the vortex lattice, the creation of new vortex-liquid phases, and the appearance of macroscopic quantum phenomena. Introducing quenched disorder into the system turns the Abrikosov lattice into a vortex glass, whereas the vortex liquid remains a liquid. The terms "glass" and "liquid" are defined in a dynamic sense, with a sublinear response $\ensuremath{\rho}={\frac{\ensuremath{\partial}E}{\ensuremath{\partial}j}|}_{j\ensuremath{\rightarrow}0}$ characterizing the truly superconducting vortex glass and a finite resistivity $\ensuremath{\rho}(j\ensuremath{\rightarrow}0)g0$ being the signature of the liquid phase. The smallness of $\frac{{j}_{c}}{{j}_{o}}$ allows one to discuss the influence of quenched disorder in terms of the weak collective pinning theory. Supplementing the traditional theory of weak collective pinning to take into account thermal and quantum fluctuations, as well as the new scaling concepts for elastic media subject to a random potential, this modern version of the weak collective pinning theory consistently accounts for a large number of novel phenomena, such as the broad resistive transition, thermally assisted flux flow, giant and quantum creep, and the glassiness of the solid state. The strong layering of the oxides introduces additional new features into the thermodynamic phase diagram, such as a layer decoupling transition, and modifies the mechanism of pinning and creep in various ways. The presence of strong (correlated) disorder in the form of twin boundaries or columnar defects not only is technologically relevant but also provides the framework for the physical realization of novel thermodynamic phases such as the Bose glass. On a macroscopic scale the vortex system exhibits self-organized criticality, with both the spatial and the temporal scale accessible to experimental investigations.

4,502 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed and self-contained presentation of the replica theory of infinite range spin glasses is presented, paying particular attention to new applications in the study of optimization theory and neural networks.
Abstract: This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular attention to new applications in the study of optimization theory and neural networks. About two-thirds of the book are a collection of the most interesting and pedagogical articles on the subject.

3,846 citations


"Disordered elastic systems and one-..." refers methods in this paper

  • ...We first used the so-called ‘replica trick’, well-known in the study of spin glasses [39], in order to average first over the disorder and so to transform the random part Hdis in the full Hamiltonian of one interface (u1), into an effective non-random coupling between n copies of the interface (u1⁄4 fu1, ....

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  • ...The two main analytical tools used on DES are on one hand the Functional Renormalization Group (FRG) where the whole disorder correlator (3) evolves under the renormalization procedure [17,34–37], and on the other hand the Gaussian Variational Method (GVM) as introduced by Mézard and Parisi on DES, and involving Replica to treat the disorder [38,39]....

    [...]

Journal ArticleDOI
TL;DR: In many materials with a highly anisotropic band structure, electron-phonon interactions lead to a novel type of ground state called the charge-density wave as mentioned in this paper, which can, even for small electric fields, carry current in a fashion originally envisioned by Frohlich.
Abstract: In many materials with a highly anisotropic band structure, electron-phonon interactions lead to a novel type of ground state called the charge-density wave. The condensate is pinned to the underlying lattice by impurities and by boundary effects, but can, even for small electric fields, carry current in a fashion originally envisioned by Fr\"ohlich. This review discusses some of the underlying theories and the main experimental observations on this new collective transport phenomenon. The frequency- and electric-field-dependent conductivity, current oscillations, electric-field-dependent transport coefficients and elastic properties, together with nuclear-magnetic-resonance experiments, provide clear evidence for a translational motion of the condensate. Various theories, involving classical and quantum-mechanical concepts, are able to account for a broad variety of experimental findings, which were also made in the presence of combined dc and ac fields.

1,308 citations


"Disordered elastic systems and one-..." refers background in this paper

  • ...ferroelectric [1, 2, 3] or ferromagnetic [4, 5, 6] domain walls, contact line in wetting experiments [7] or propagating cracks in paper and thin materials [8]) or periodic systems (typically vortex lattices in type-II superconductors [9], classical [10] or quantum [11] Wigner crystals, or electronic crystals displaying charge or spin density waves [12, 13])....

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Journal ArticleDOI
TL;DR: Kinetic interfaces form the basis of a fascinating, interdisciplinary branch of statistical mechanics as mentioned in this paper, which can be unified via an intriguing nonlinear stochastic partial differential equation whose consequences and generalizations have mobilized a sizeable community of physicists concerned with a statistical description of kinetically roughened surfaces.

1,015 citations