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Sep 22, 2013
09/13

by
Pierre Le Doussal

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We study the Sinai model for the diffusion of a particle in a one dimension random potential in presence of a small concentration $\rho$ of perfect absorbers using the asymptotically exact real space renormalization method. We compute the survival probability, the averaged diffusion front and return probability, the two particle meeting probability, the distribution of total distance traveled before absorption and the averaged Green's function of the associated Schrodinger operator. Our work...

Source: http://arxiv.org/abs/0906.0267v1

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Sep 18, 2013
09/13

by
Pierre Le Doussal

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Some aspects of the functional RG (FRG) approach to pinned elastic manifolds (of internal dimension $d$) at finite temperature $T>0$ are reviewed and reexamined in this much expanded version of [Europhys. Lett. {\bf 76} 457 (2006)]. The particle limit $d=0$ provides a test for the theory: there the FRG is equivalent to the decaying Burgers equation, with viscosity $\nu \sim T$ - both being formally irrelevant. Analogy between Kolmogorov scaling and FRG cumulant scaling is discussed. Next we...

Source: http://arxiv.org/abs/0809.1192v1

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Sep 18, 2013
09/13

by
Pierre Le Doussal

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We study, using functional renormalization (FRG), two copies of an elastic system pinned by mutually correlated random potentials. Short scale decorrelation depend on a non trivial boundary layer regime with (possibly multiple) chaos exponents. Large scale mutual displacement correlation behave as $|x-x'|^{2 \zeta - \mu}$, the decorrelation exponent $\mu$ proportional to the difference between Flory (or mean field) and exact roughness exponent $\zeta$. For short range disorder $\mu >0$ but...

Source: http://arxiv.org/abs/cond-mat/0505679v2

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Jun 30, 2018
06/18

by
Pierre Le Doussal

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We show how our previous result based on the replica Bethe ansatz for the Kardar Parisi Zhang (KPZ) equation with the "half-flat" initial condition leads to the Airy$_2$ to Airy$_1$ (i.e. GUE to GOE) universal crossover one-point height distribution in the limit of large time. Equivalently, we obtain the distribution of the free energy of a long directed polymer (DP) in a random potential with one fixed endpoint and the other one on a half-line. We then generalize to a DP when each...

Topics: Statistical Mechanics, Mathematics, Mathematical Physics, Disordered Systems and Neural Networks,...

Source: http://arxiv.org/abs/1401.1081

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Sep 18, 2013
09/13

by
Pierre Le Doussal

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The functional RG (FRG) approach to pinning of $d$-dimensional manifolds is reexamined at any temperature $T$. A simple relation between the coupling function $R(u)$ and a physical observable is shown in any $d$. In $d=0$ its beta function is displayed to a high order, ambiguities resolved; for random field disorder (Sinai model) we obtain exactly the T=0 fixed point $R(u)$ as well as its thermal boundary layer (TBL) form (i.e. for $u \sim T$) at $T>0$. Connection between FRG in $d=0$ and...

Source: http://arxiv.org/abs/cond-mat/0605490v1

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Jul 20, 2013
07/13

by
David Carpentier; Pierre Le Doussal

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We study 2D solids with weak substrate disorder, using Coulomb gas renormalisation. The melting transition is found to be replaced by a sharp crossover between a high $T$ liquid with thermally induced dislocations, and a low $T$ glassy regime with disorder induced dislocations at scales larger than $\xi_{d}$ which we compute ($\xi_{d}\gg R_{c}\sim R_{a}$, the Larkin and translational correlation lengths). We discuss experimental consequences, reminiscent of melting, such as size effects in...

Source: http://arxiv.org/abs/cond-mat/9712227v1

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Sep 18, 2013
09/13

by
Christian Hagendorf; Pierre Le Doussal

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Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE_k with parameter k = 2. In this note, some properties of an SLE_k trace on doubly-connected domains are studied and a connection to passive scalar diffusion in a Burgers flow is emphasised. In particular, the endpoint probability distribution and winding probabilities for SLE_2 on a cylinder, starting from one boundary component and stopped when hitting...

Source: http://arxiv.org/abs/0803.3249v1

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Sep 18, 2013
09/13

by
Cecile Monthus; Pierre Le Doussal

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We consider the Sinai model describing a particle diffusing in a 1D random force field. As shown by Golosov, this model exhibits a strong localization phenomenon for the thermal packet: the disorder average of the thermal distribution of the relative distance y=x-m(t), with respect to the (disorder-dependent) most probable position m(t), converges in the limit of infinite time towards a distribution P(y). In this paper, we revisit this question of the localization of the thermal packet. We...

Source: http://arxiv.org/abs/cond-mat/0202295v1

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Sep 23, 2013
09/13

by
David Carpentier; Pierre Le Doussal

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We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the transition at which frozen topological defects (vortices) proliferate. This RG approach is constructed both from the replicated Coulomb gas and, equivalently without the use of replicas, using the probability distribution of the local disorder (random defect core...

Source: http://arxiv.org/abs/cond-mat/9908335v1

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Sep 20, 2013
09/13

by
Pierre Le Doussal; Gregory Schehr

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Using functional RG, we reexamine the glass phase of the 2D random-field Sine Gordon model. It is described by a line of fixed points (FP) with a super-roughening amplitude $\bar{(u(0)-u(r))^2} \sim A(T) \ln^2 r $ as temperature $T$ is varied. A speculation is that this line is identical to the one found in disordered free-fermion models via exact results from ``nearly conformal'' field theory. This however predicts $A(T=0)=0$, contradicting numerics. We point out that this result may be...

Source: http://arxiv.org/abs/cond-mat/0607657v2

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Sep 22, 2013
09/13

by
Leon Balents; Pierre Le Doussal

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We study thermally activated dynamics using functional renormalization within the field theory of randomly pinned elastic systems, a prototype for glasses. It appears through an essentially non-perturbative boundary layer in the running effective action, for which we find a consistent scaling ansatz to all orders. We find that in the statics the boundary layer describes the physics of rare low energy metastable states as suggested by a phenomenological droplet picture. The extension to...

Source: http://arxiv.org/abs/cond-mat/0205358v1

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Sep 21, 2013
09/13

by
Pasquale Calabrese; Pierre Le Doussal

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We provide the first exact calculation of the height distribution at arbitrary time $t$ of the continuum KPZ growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer (DP) with one end fixed, one free, and the Bethe Ansatz for the replicated attractive boson model. We obtain the generating function of the moments of the DP partition sum as a Fredholm Pfaffian. Our formula, valid for all times, exhibits convergence of the free energy (i.e. KPZ...

Source: http://arxiv.org/abs/1104.1993v1

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Sep 18, 2013
09/13

by
David Carpentier; Pierre Le Doussal

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We present a detailed derivation of the renormalization group equations for two dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between the charges involve both angular couplings and a new electromagnetic potential. This motivates the denomination of ``elastic'' Coulomb gas. Such elastic Coulomb gases arise naturally in the study of the continuous melting transition of two dimensional solids...

Source: http://arxiv.org/abs/0707.2667v1

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Sep 19, 2013
09/13

by
Gregory Schehr; Pierre Le Doussal

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We use the Real Space Renormalization Group (RSRG) method to study extreme value statistics for a variety of Brownian motions, free or constrained such as the Brownian bridge, excursion, meander and reflected bridge, recovering some standard results, and extending others. We apply the same method to compute the distribution of extrema of Bessel processes. We briefly show how the continuous time random walk (CTRW) corresponds to a non standard fixed point of the RSRG transformation.

Source: http://arxiv.org/abs/0910.4913v1

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Sep 19, 2013
09/13

by
Cecile Monthus; Pierre Le Doussal

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We study the time dependent potential energy $W(t)=U(x(0)) - U(x(t))$ of a particle diffusing in a one dimensional random force field (the Sinai model). Using the real space renormalization group method (RSRG), we obtain the exact large time limit of the probability distribution of the scaling variable $w=W(t)/(T \ln t)$. This distribution exhibits a {\it nonanalytic} behaviour at $w=1$. These results are extended to a small non-zero applied field. Using the constrained path integral method, we...

Source: http://arxiv.org/abs/cond-mat/0206035v1

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Sep 18, 2013
09/13

by
Horacio Castillo; Pierre Le Doussal

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A particle in a random potential with logarithmic correlations in dimensions $d=1,2$ is shown to undergo a dynamical transition at $T_{dyn}>0$. In $d=1$ exact results demonstrate that $T_{dyn}=T_c$, the static glass transition temperature, and that the dynamical exponent changes from $z(T)=2 + 2 (T_c/T)^2$ at high temperature to $z(T)= 4 T_c/T$ in the glass phase. The same formulae are argued to hold in $d=2$. Dynamical freezing is also predicted in the 2D random gauge XY model and related...

Source: http://arxiv.org/abs/cond-mat/0006373v1

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Sep 22, 2013
09/13

by
Gregory Schehr; Pierre Le Doussal

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Using one loop functional RG we study two problems of pinned elastic systems away from their equilibrium or steady states. The critical regime of the depinning transition is investigated starting from a flat initial condition. It exhibits non trivial two-time dynamical regimes with exponents and scaling functions obtained in a dimensional expansion. The aging and equilibrium dynamics of the super-rough glass phase of the random Sine-Gordon model at low temperature is found to be characterized...

Source: http://arxiv.org/abs/cond-mat/0501199v1

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Jun 29, 2018
06/18

by
Thimothée Thiery; Pierre Le Doussal

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Quantifying the universality of avalanche observables beyond critical exponents is of current great interest in theory and experiments. Here, we improve the characterization of the spatio-temporal process inside avalanches in the universality class of the depinning of elastic interfaces in random media. Surprisingly, at variance with the temporal shape, the spatial shape of avalanches has not yet been predicted. In part this is due to a lack of an analytically tractable definition: how should...

Topics: Disordered Systems and Neural Networks, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1601.00174

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Sep 20, 2013
09/13

by
Gregory Schehr; Pierre Le Doussal

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We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the $\eta$ exponent and scaling functions. Then it is applied to study...

Source: http://arxiv.org/abs/cond-mat/0304486v1

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Sep 23, 2013
09/13

by
Thierry Giamarchi; Pierre Le Doussal

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We study periodic lattices, such as vortex lattices, driven by an external force in a random pinning potential. We show that effects of static disorder persist even at large velocity. It results in a novel moving glass state with topological order analogous to the static Bragg glass. The lattice flows through well-defined, elastically coupled, {\it % static} channels. We predict barriers to transverse motion resulting in finite transverse critical current. Experimental tests of the theory are...

Source: http://arxiv.org/abs/cond-mat/9512006v2

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Jun 30, 2018
06/18

by
Thimothée Thiery; Pierre Le Doussal

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We study the model of a discrete directed polymer (DP) on the square lattice with homogeneous inverse gamma distribution of site random Boltzmann weights, introduced by Seppalainen. The integer moments of the partition sum, $\overline{Z^n}$, are studied using a transfer matrix formulation, which appears as a generalization of the Lieb-Liniger quantum mechanics of bosons to discrete time and space. In the present case of the inverse gamma distribution the model is integrable in terms of a...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1406.5963

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Sep 18, 2013
09/13

by
Thierry Giamarchi; Pierre Le Doussal

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We apply the gaussian variational method (GVM) to study the equilibrium statistical mechanics of the two related systems: (i) classical elastic manifolds, such as flux lattices, in presence of columnar disorder correlated along the $\tau$ direction (ii) interacting quantum particles in a static random potential. We find localization by disorder, the localized phase being described by a replica symmetry broken solution confined to the mode $\omega=0$. For classical systems we compute the...

Source: http://arxiv.org/abs/cond-mat/9509008v1

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Sep 18, 2013
09/13

by
Pascal Chauve; Pierre Le Doussal

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We develop a systematic multi-local expansion of the Polchinski-Wilson exact renormalization group (ERG) equation. Integrating out explicitly the non local interactions, we reduce the ERG equation obeyed by the full interaction functional to a flow equation for a function, its local part. This is done perturbatively around fixed points, but exactly to any given order in the local part. It is thus controlled, at variance with projection methods, e.g. derivative expansions or local potential...

Source: http://arxiv.org/abs/cond-mat/0006057v1

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Sep 20, 2013
09/13

by
Baruch Horovitz; Pierre Le Doussal

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A layered system of charges with logarithmic interaction parallel to the layers and random dipoles in each layer is studied via a variational method and an energy rationale. These methods reproduce the known phase diagram for a single layer where charges unbind by increasing either temperature or disorder, as well as a freezing first order transition within the ordered phase. Increasing interlayer coupling leads to successive transitions in which charge rods correlated in N>1 neighboring...

Source: http://arxiv.org/abs/cond-mat/0410019v2

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Sep 17, 2013
09/13

by
Baruch Horovitz; Pierre Le Doussal

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Using an exact mapping to disordered Coulomb gases, we introduce a novel method to study two dimensional Dirac fermions with quenched disorder in two dimensions which allows to treat non perturbative freezing phenomena. For purely random gauge disorder it is known that the exact zero energy eigenstate exhibits a freezing-like transition at a threshold value of disorder $\sigma=\sigma_{th}=2$. Here we compute the dynamical exponent $z$ which characterizes the critical behaviour of the density of...

Source: http://arxiv.org/abs/cond-mat/0108143v1

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Sep 21, 2013
09/13

by
Laurent Laloux; Pierre Le Doussal

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We study out of equilibrium dynamics and aging for a particle diffusing in one dimensional environments, such as the random force Sinai model, as a toy model for low dimensional systems. We study fluctuations of two times $(t_w, t)$ quantities from the probability distribution $Q(z,t,t_w)$ of the relative displacement $z = x(t) - x(t_w)$ in the limit of large waiting time $t_w \to \infty$ using numerical and analytical techniques. We find three generic large time regimes: (i) a...

Source: http://arxiv.org/abs/cond-mat/9705249v1

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Sep 20, 2013
09/13

by
Pierre Le Doussal; Thierry Giamarchi

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We discuss the question of the generation of topological defects (dislocations) by quenched disorder in two dimensional periodic systems. In a previous study [Phys. Rev. B {\bf 52} 1242 (1995)] we found that, contrarily to $d=3$, unpaired dislocations appear in $d=2$ above a length scale $\xi_D$, which we estimated. We extend this description to include effects of freezing and pinning of dislocations at low temperature. The resulting $\xi_D$ at low temperature is found to be {\it larger} than...

Source: http://arxiv.org/abs/cond-mat/9810218v1

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Sep 22, 2013
09/13

by
Gregory Schehr; Pierre Le Doussal

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Using RG we investigate the non-equilibrium relaxation of the (Cardy-Ostlund) 2D random Sine-Gordon model, which describes pinned arrays of lines. Its statics exhibits a marginal ($\theta=0$) glass phase for $T

Source: http://arxiv.org/abs/cond-mat/0403382v3

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Sep 20, 2013
09/13

by
David Carpentier; Pierre Le Doussal

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We study two dimensional triangular elastic lattices in a background of point disorder, excluding dislocations (tethered network). Using both (replica symmetric) static and (equilibrium) dynamic renormalization group for the corresponding $N=2$ component model, we find a transition to a glass phase for $T < T_g$, described by a plane of perturbative fixed points. The growth of displacements is found to be asymptotically isotropic with $u_T^2 \sim u_L^2 \sim A_1 \ln^2 r$, with universal...

Source: http://arxiv.org/abs/cond-mat/9611168v1

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Sep 23, 2013
09/13

by
Pierre Le Doussal; Thierry Giamarchi

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We study periodic structures, such as vortex lattices, moving in a random potential. As predicted in [T. Giamarchi, P. Le Doussal Phys. Rev. Lett. 76 3408 (1996)] the periodicity in the direction transverse to motion leads to a new class of driven systems: the Moving Glasses. We analyse using several RG techniques the properties at T=0 and $T>0$: (i) decay of translational long range order (ii) particles flow along static channels (iii) the channel pattern is highly correlated (iv) barriers...

Source: http://arxiv.org/abs/cond-mat/9708085v1

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Sep 21, 2013
09/13

by
Pierre Le Doussal; Pasquale Calabrese

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We study the directed polymer (DP) of length $t$ in a random potential in dimension 1+1 in the continuum limit, with one end fixed and one end free. This maps onto the Kardar-Parisi-Zhang growth equation in time $t$, with flat initial conditions. We use the Bethe Ansatz solution for the replicated problem which is an attractive bosonic model. The problem is more difficult than the previous solution of the fixed endpoint problem as it requires regularization of the spatial integrals over the...

Source: http://arxiv.org/abs/1204.2607v1

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Jun 29, 2018
06/18

by
Thimothé Thiery; Pierre Le Doussal

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We consider the Beta polymer, an exactly solvable model of directed polymer on the square lattice, introduced by Barraquand and Corwin. We study the statistical properties of its point to point partition sum. The problem is equivalent to a model of a random walk in a time-dependent (and in general biased) 1D random environment. In this formulation, we study the sample to sample fluctuations of the transition probability distribution function (PDF) of the random walk. Using the Bethe ansatz we...

Topics: Disordered Systems and Neural Networks, Statistical Mechanics, Condensed Matter, Mathematical...

Source: http://arxiv.org/abs/1605.07538

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Sep 21, 2013
09/13

by
Baruch Horovitz; Pierre Le Doussal

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We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. We analyze our solution within a renormalization group (RG) scheme to all orders which reproduces a 2 loop RG for the Caldeira-Legget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in -R^2 where R is the ring's radius. For either a charge or an electric dipole coupled to a dirty metal we find that...

Source: http://arxiv.org/abs/cond-mat/0602391v2

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Sep 23, 2013
09/13

by
Thierry Giamarchi; Pierre Le Doussal

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It was shown in our Letter that the novel glassy property of the moving lattice (transverse critical force and pinned channels) originate {\it only} from the periodicity in the {\it transverse} direction, i.e the underlying smectic density modes of the structure. Thus, contrarily to the claim of the Comment, these properties should be robust to the details of the structure along the direction of motion, even in the presence of a random force (we have demonstrated the existence of a random force...

Source: http://arxiv.org/abs/cond-mat/9608153v1

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Sep 21, 2013
09/13

by
Thierry Giamarchi; Pierre Le Doussal

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We examine here various aspects of the statics and dynamics of disordered elastic systems such as manifolds and periodic systems. Although these objects look very similar and indeed share some underlying physics, periodic systems constitute a class of their own with markedly different properties. We focus on such systems, review the methods allowing to treat them, emphasize the shift of viewpoint compared to the physics of manifolds and discuss their physics in detail. As for the statics,...

Source: http://arxiv.org/abs/cond-mat/9705096v1

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Sep 20, 2013
09/13

by
David Carpentier; Pierre Le Doussal

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We present a novel RG approach to 2D random XY models using direct and replicated Coulomb gas methods. By including fusion of environments (charge fusion in the replicated CG) it follows the distribution of local disorder, found to obey a Kolmogorov non linear equation (KPP) with traveling wave solutions. At low T and weak disorder it yields a glassy XY phase with broad distributions and precise connections to Derrida's GREM. Finding marginal operators at the disorder-induced transition is...

Source: http://arxiv.org/abs/cond-mat/9802083v2

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Sep 23, 2013
09/13

by
Baruch Horovitz; Pierre Le Doussal

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We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. Our solution produces a renormalization group (RG) transformation to all orders in the inverse dissipation strength, and in particular reproduces known two loop results. Our RG leads to a weak dissipation parameter, for which a weak coupling expansion for the position correlation function shows a 1/t^2 decay in imaginary time.

Source: http://arxiv.org/abs/1006.4125v1

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Sep 21, 2013
09/13

by
Cecile Monthus; Pierre Le Doussal

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The thermal fluctuations that exist at very low temperature in disordered systems are often attributed to the existence of some two-level excitations. In this paper, we revisit this question via the explicit studies of the following 1D models (i) a particle in 1D random potentials (ii) the random field Ising chain with continuous disorder distribution. In both cases, we define precisely the `two-level' excitations and their statistical properties, and we show that their contributions to various...

Source: http://arxiv.org/abs/cond-mat/0407289v1

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Sep 23, 2013
09/13

by
Leon Balents; Pierre Le Doussal

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Using the functional renormalization group (FRG) we study the thermal fluctuations of elastic objects, described by a displacement field u and internal dimension d, pinned by a random potential at low temperature T, as prototypes for glasses. A challenge is how the field theory can describe both typical (minimum energy T=0) configurations, as well as thermal averages which, at any non-zero T as in the phenomenological droplet picture, are dominated by rare degeneracies between low lying minima....

Source: http://arxiv.org/abs/cond-mat/0408048v1

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Sep 20, 2013
09/13

by
Pierre Le Doussal; Leo Radzihovsky

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We study $D$-dimensional polymerized membranes embedded in $d$ dimensions using a self-consistent screening approximation. It is exact for large $d$ to order $1/d$, for any $d$ to order $\epsilon=4-D$ and for $d=D$. For flat physical membranes ($D=2,d=3$) it predicts a roughness exponent $\zeta=0.590$. For phantom membranes at the crumpling transition the size exponent is $\nu=0.732$. It yields identical lower critical dimension for the flat phase and crumpling transition $D_{lc}(d)={2 d \over...

Source: http://arxiv.org/abs/cond-mat/9208023v1

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Sep 18, 2013
09/13

by
Baruch Horovitz; Pierre Le Doussal

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A 3D layered system of charges with logarithmic interaction parallel to the layers and random dipoles is studied via a novel variational method and an energy rationale which reproduce the known phase diagram for a single layer. Increasing interlayer coupling leads to successive transitions in which charge rods correlated in N>1 neighboring layers are nucleated by weaker disorder. For layered superconductors in the limit of only magnetic interlayer coupling, the method predicts and locates a...

Source: http://arxiv.org/abs/cond-mat/0002037v1

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Sep 23, 2013
09/13

by
Leon Balents; Pierre Le Doussal

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We study thermally activated, low temperature equilibrium dynamics of elastic systems pinned by disorder using one loop functional renormalization group (FRG). Through a series of increasingly complete approximations, we investigate how the field theory reveals the glassy nature of the dynamics, in particular divergent barriers and barrier distributions controling the spectrum of relaxation times. A naive single relaxation time approximation for each wavevector is found to be unsatisfactory. A...

Source: http://arxiv.org/abs/cond-mat/0312338v1

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Sep 22, 2013
09/13

by
David Carpentier; Pierre Le Doussal

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We study via RG, numerics, exact bounds and qualitative arguments the equilibrium Gibbs measure of a particle in a $d$-dimensional gaussian random potential with {\it translationally invariant logarithmic} spatial correlations. We show that for any $d \ge 1$ it exhibits a transition at $T=T_c>0$. The low temperature glass phase has a non trivial structure, being dominated by {\it a few} distant states (with replica symmetry breaking phenomenology). In finite dimension this transition exists...

Source: http://arxiv.org/abs/cond-mat/0003281v1

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Jun 29, 2018
06/18

by
Xiangyu Cao; Pierre Le Doussal

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We calculate the joint min--max distribution and the Edwards-Anderson's order parameter for the circular model of $1 / f$-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We...

Topics: Disordered Systems and Neural Networks, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1604.02282

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Sep 18, 2013
09/13

by
Pierre Le Doussal; Cecile Monthus

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We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random local bias (Sinai model) and react upon meeting. We obtain the large time decay of the density of each specie, their associated universal amplitudes, and the spatial distribution of particles. We also derive the spectrum of exponents which characterize the...

Source: http://arxiv.org/abs/cond-mat/9901306v1

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19

Jun 28, 2018
06/18

by
Thimothée Thiery; Pierre Le Doussal

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In a recent work Povolotsky provided a three-parameter family of stochastic particle systems with zero-range interactions in one dimension which are integrable by coordinate Bethe ansatz. Using these results we obtain the corresponding condition for integrability of a class of directed polymer models with random weights on the square lattice. Analyzing the solutions we find, besides known cases, a new two-parameter family of integrable DP model, which we call the Inverse-Beta polymer, and...

Topics: Disordered Systems and Neural Networks, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1506.05006

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10.0

Jun 30, 2018
06/18

by
Pasquale Calabrese; Pierre Le Doussal

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Recent exact solutions of the 1D Kardar-Parisi-Zhang equation make use of the 1D integrable Lieb-Liniger model of interacting bosons. For flat initial conditions, it requires the knowledge of the overlap between the uniform state and arbitrary exact Bethe eigenstates. The same quantity is also central in the study of the quantum quench from a 1D non-interacting Bose-Einstein condensate upon turning interactions. We compare recent advances in both domains, i.e. our previous exact solution, and a...

Topics: Statistical Mechanics, Disordered Systems and Neural Networks, Quantum Gases, Mathematics,...

Source: http://arxiv.org/abs/1402.1278

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51

Sep 22, 2013
09/13

by
Pierre Le Doussal; Kay Jörg Wiese

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We study the dynamics of polymers and elastic manifolds in non potential static random flows. We find that barriers are generated from combined effects of elasticity, disorder and thermal fluctuations. This leads to glassy trapping even in pure barrier-free divergenceless flows $v {f \to 0}{\sim} f^\phi$ ($\phi > 1$). The physics is described by a new RG fixed point at finite temperature. We compute the anomalous roughness $R \sim L^\zeta$ and dynamical $t\sim L^z$ exponents for directed and...

Source: http://arxiv.org/abs/cond-mat/9708112v1

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62

Sep 20, 2013
09/13

by
Pierre Le Doussal; Kay Joerg Wiese

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In this note, we clarify the stability of the large-N functional RG fixed points of the order/disorder transition in the random-field (RF) and random-anisotropy (RA) O(N) models. We carefully distinguish between infinite N, and large but finite N. For infinite N, the Schwarz-Soffer inequality does not give a useful bound, and all fixed points found in cond-mat/0510344 (Phys. Rev. Lett. 96, 197202 (2006)) correspond to physical disorder. For large but finite N (i.e. to first order in 1/N) the...

Source: http://arxiv.org/abs/cond-mat/0612310v1

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118

Sep 23, 2013
09/13

by
Pierre Le Doussal; Kay Joerg Wiese

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We study the energy minimization problem for an elastic interface in a random potential plus a quadratic well. As the position of the well is varied, the ground state undergoes jumps, called shocks or static avalanches. We introduce an efficient and systematic method to compute the statistics of avalanche sizes and manifold displacements. The tree-level calculation, i.e. mean-field limit, is obtained by solving a saddle-point equation. Graphically, it can be interpreted as a the sum of all tree...

Source: http://arxiv.org/abs/1111.3172v1