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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Dissertation•
01 Jan 2013
TL;DR: In this article, it is observed that leur rugosite ainsi que leur reponse dynamique suivent des lois d'echelles doublement influencees par la nature du desordre and les conditions environnementales.
Abstract: Les materiaux ferroelectriques sont caracterises par une polarisation electrique reversible. Les interfaces separant deux domaines ferroelectriques, appelees parois de domaines, possedent des proprietes specifiques en raison de la brisure locale de symetrie et de l'accumulation de defauts, et ce a l'echelle nanometrique. Cette these presente plusieurs de ces proprietes, mesurees par microscopie a force atomique sur des ferroelectriques en couches minces. En premier lieu, il est demontre que la brisure de symetrie modifie les proprietes piezoelectriques aux parois. Puis il est demontre que, bien que le ferroelectrique soit isolant, les parois autorisent le transport de courant electrique via l'accumulation de lacunes d'oxygene. La seconde partie de cette these porte sur les proprietes statiques et dynamiques des parois dans le cadre theorique d'interfaces elastiques desordonnees. Il est observe que leur rugosite ainsi que leur reponse dynamique suivent des lois d'echelles doublement influencees par la nature du desordre et les conditions environnementales.
9 citations
Cites background from "Disordered elastic systems and one-..."
...Néel and Bloch domain walls) and absent from most models, has recently been addressed and demonstrated to have a crucial impact on the interface properties [98]....
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...In this case, the interface formed by the domain wall can thus be described by the very general model of a fluctuating elastic manifold in a disordered medium [12, 98]....
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TL;DR: In this paper, a model system of a long-range elastic line driven in a random landscape is considered and the critical force is computed perturbatively in the collective pinning regime.
Abstract: We address the eect of disorder geometry on the critical force in disordered elastic systems. We focus on the model system of a long-range elastic line driven in a random landscape. In the collective pinning regime, we compute the critical force perturbatively. Not only does our expression for the critical force conrm previous results on its scaling with respect to the microscopic disorder parameters, but it also provides its precise dependence on the disorder geometry (represented by the disorder two-point correlation function). Our results are successfully compared with the results of numerical simulations for random eld and random bond disorders.
8 citations
Cites background from "Disordered elastic systems and one-..."
...Disordered elastic systems [1]–[4] are ubiquitous in Nature and condensed matter physics; they encompass a wide range of systems going from vortex lattices in superconductors [5] to ferromagnetic domain walls [6], wetting fronts [7], imbibition fronts [8, 9] or crack fronts in brittle solids [10, 11]....
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...Any positive stiffness rounds the transition, analogously to the temperature [4, 14, 31]....
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...As a result of the competition between disorder and elasticity, the elastic object becomes rough and is characterized by a universal roughness exponent [12, 13] that depends on the dimension of the problem, the range of the elastic interaction and the type of disorder, but not on the microscopic details of the system [2, 4]....
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TL;DR: In this paper, the effect of temperature on the yielding transition of amorphous solids was analyzed using different coarse-grained model approaches, such as the Prandtl-Tomlinson model and the Langevin stochastic force.
Abstract: We analyze the effect of temperature on the yielding transition of amorphous solids using different coarse-grained model approaches. On one hand, we use an elastoplastic model, with temperature introduced in the form of an Arrhenius activation law over energy barriers. On the other hand, we implement a Hamiltonian model with a relaxational dynamics, where temperature is introduced in the form of a Langevin stochastic force. In both cases, temperature transforms the sharp transition of the athermal case in a smooth crossover. We show that this thermally smoothed transition follows a simple scaling form that can be fully explained using a one-particle system driven in a potential under the combined action of a mechanical and a thermal noise, namely, the stochastically driven Prandtl-Tomlinson model. Our work harmonizes the results of simple models for amorphous solids with the phenomenological $\ensuremath{\sim}{T}^{2/3}$ law proposed by Johnson and Samwer [Phys. Rev. Lett. 95, 195501 (2005)] in the framework of experimental metallic glasses yield observations, and extend it to a generic case. Conclusively, our results strengthen the interpretation of the yielding transition as an effective mean-field phenomenon.
7 citations
TL;DR: In this paper, the authors focus on the mean velocity induced by a constant force applied on one-dimensional interfaces and propose an effective model with two degrees of freedom, constructed from the full spatially extended model, that captures many aspects of the creep phenomenology.
Abstract: The response of spatially extended systems to a force leading their steady state out of equilibrium is strongly affected by the presence of disorder. We focus on the mean velocity induced by a constant force applied on one-dimensional interfaces. In the absence of disorder, the velocity is linear in the force. In the presence of disorder, it is widely admitted, as well as experimentally and numerically verified, that the velocity presents a stretched exponential dependence in the force (the so-called 'creep law'), which is out of reach of linear response, or more generically of direct perturbative expansions at small force. In dimension one, there is no exact analytical derivation of such a law, even from a theoretical physical point of view. We propose an effective model with two degrees of freedom, constructed from the full spatially extended model, that captures many aspects of the creep phenomenology. It provides a justification of the creep law form of the velocity-force characteristics, in a quasistatic approximation. It allows, moreover, to capture the non-trivial effects of short-range correlations in the disorder, which govern the low-temperature asymptotics. It enables us to establish a phase diagram where the creep law manifests itself in the vicinity of the origin in the force--system-size--temperature coordinates. Conjointly, we characterise the crossover between the creep regime and a linear-response regime that arises due to finite system size.
7 citations
Cites background or methods from "Disordered elastic systems and one-..."
...For the moment, we will simply use the fact that the amplitude D̃ retains the dependence in ξ of the disorder free-energy, which manifests itself at scales much larger than ξ itself [11,38,51]....
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...Here, Tc is a characteristic temperature that separates these two asymptotic regimes, and D̃ presents a smooth crossover between them, predicted analytically using a variational scheme [37,39] and observed numerically [38,52]....
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...The dependence in the original correlation length ξ is absorbed in the common prefactor to all terms of (47), through the constant D̃ [11,37,38]....
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...where D̃ is the “amplitude” of the disorder free energy two-point correlator [11,38,51] at large tf....
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26 Oct 2020
TL;DR: In this paper, the magnetic-field-driven motion of domain walls with different chiralities in thin ferromagnetic films made of Pt/Co/Pt, Au/Co /Pt and Pt /Co/Au was explored.
Abstract: We explore the magnetic-field-driven motion of domain walls with different chiralities in thin ferromagnetic films made of Pt/Co/Pt, Au/Co/Pt, and Pt/Co/Au. From the analysis of domain wall dynamics, we extract parameters characterizing the interaction between domain walls and weak pinning disorder of the films. The variations of domain wall structure, controlled by an in-plane field, are found to modify the characteristic length scale of pinning in strong correlation with the domain wall width, whatever its chirality and the interaction strength between domain walls and pinning defects. These findings should be also relevant for a wide variety of elastic interfaces moving in weak pinning disordered media
7 citations
References
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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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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
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]....
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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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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