arXiv subjects

Pierre Le Doussal

Publications and source records attributed to Pierre Le Doussal.

At least 217 records · Page 12Linked to original sources

arXiv2007

Electromagnetic Coulomb Gas with Vector Charges and "Elastic'' Potentials : Renormalization Group Equations

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 coupled to a substrate, either commensurate or with quenched disorder.

cond-mat.stat-mech↗

arXiv2007

Disordered free fermions and the Cardy Ostlund fixed line at low temperature

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 related to failure of dimensional reduction, and that a functional RG method incorporating higher harmonics and non-analytic operators predicts a non-zero $A(T=0)$ which compares reasonably with numerics.

cond-mat.dis-nn↗

arXiv2007

Statics and dynamics of elastic manifolds in media with long-range correlated disorder

We study the statics and dynamics of an elastic manifold in a disordered medium with quenched defects correlated as r^{-a} for large separation r. We derive the functional renormalization-group equations to one-loop order, which allow us to describe the universal properties of the system in equilibrium and at the depinning transition. Using a double epsilon=4-d and delta=4-a expansion, we compute the fixed points characterizing different universality classes and analyze their regions of stability. The long-range disorder-correlator remains analytic but generates short-range disorder whose correlator exhibits the usual cusp. The critical exponents and universal amplitudes are computed to first order in epsilon and delta at the fixed points. At depinning, a velocity-versus-force exponent beta larger than unity can occur. We discuss possible realizations using extended defects.

cond-mat.dis-nn↗

arXiv2006

Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?

Domain walls for spin glasses are believed to be scale invariant invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to test the hypothesis that these domain walls are described by a Schramm-Loewner evolution SLE$_κ$. Multiple tests are consistent with SLE$_κ$, where $κ=2.30(5)$. Both conformal invariance and the domain Markov property are tested. The latter does not hold in small systems, but detailed numerical evidence suggests that it holds in the continuum limit.

cond-mat.dis-nn↗

arXiv2006

Functional Renormalization for Disordered Systems, Basic Recipes and Gourmet Dishes

We give a pedagogical introduction into the functional renormalization group treatment of disordered systems. After a review of its phenomenology, we show why in the context of disordered systems a functional renormalization group treatment is necessary, contrary to pure systems, where renormalization of a single coupling constant is sufficient. This leads to a disorder distribution, which after a finite renormalization becomes non-analytic, thus overcoming the predictions of the seemingly exact dimensional reduction. We discuss, how the non-analyticity can be measured in a simulation or experiment. We then construct a renormalizable field theory beyond leading order. We discuss an elastic manifold embedded in N dimensions, and give the exact solution for N to infinity. This is compared to predictions of the Gaussian replica variational ansatz, using replica symmetry breaking. We further consider random field magnets, and supersymmetry. We finally discuss depinning, both isotropic and anisotropic, and universal scaling function.

cond-mat.dis-nn↗

arXiv2006

Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition

We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasi-statically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the line allows to obtain the functional renormalization group (FRG) functions at the depinning transition. The universal form of the second cumulant Delta(u) is found to have a linear cusp at the origin, to be identical for RB and RF, different from the statics, and in good agreement with 2-loop FRG. The cusp is due to avalanches, which we visualize. Avalanches also produce a cusp in the third cumulant, whose universal form is obtained, as predicted by FRG.

cond-mat.dis-nn↗

arXiv2006

How to measure Functional RG fixed-point functions for dynamics and at depinning

We show how the renormalized force correlator Delta(u), the function computed in the functional RG (FRG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in presence of pinning disorder. For equilibrium dynamics we recover the relation obtained recently in the statics between Delta(u) and a physical observable. Its extension to depinning reveals interesting relations to stick-slip models of avalanches used in dry friction and earthquake dynamics. The particle limit (d=0) is solved for illustration: Delta(u) exhibits a cusp and differs from the statics. We propose that the FRG functions be measured in wetting and magnetic interfaces experiments.

cond-mat.dis-nn↗

arXiv2006

Universal distribution of threshold forces at the depinning transition

We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group (FRG) technique, we compute the distribution of pinning forces in the quasi-static limit. This distribution is universal up to two parameters, the average critical force, and its width. We discuss possible definitions for threshold forces in finite-size samples. We show how our results compare to the distribution of the latter computed recently within a numerical simulation of the so-called critical configuration.

cond-mat.dis-nn↗

arXiv2006

Wetting and Minimal Surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.

hep-th↗

arXiv2006

Measuring functional renormalization group fixed-point functions for pinned manifolds

Exact numerical minimization of interface energies is used to test the functional renormalization group (FRG) analysis for interfaces pinned by quenched disorder. The fixed-point function R(u) (the correlator of the coarse-grained disorder) is computed. In dimensions D=d+1, a linear cusp in R''(u) is confirmed for random bond (d=1,2,3), random field (d=0,2,3), and periodic (d=2,3) disorders. The functional shocks that lead to this cusp are seen. Small, but significant, deviations from 1-loop FRG results are compared to 2-loop corrections. The cross-correlation for two copies of disorder is compared with a recent FRG study of chaos.

cond-mat.dis-nn↗

arXiv2006

Interference in presence of Dissipation

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 the metal induces dissipation, however the AB amplitude is ~ R^{-2} for large R, as for free particles. Cold atoms with a large electric dipole may show a crossover between these two behaviors.

cond-mat.mes-hall↗

arXiv2006

Finite temperature Functional RG, droplets and decaying Burgers Turbulence

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 decaying Burgers is discussed. An exact solution to the functional RG hierarchy in the TBL is obtained for any $d$ and related to droplet probabilities.

cond-mat.dis-nn↗

arXiv2005

Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension

The functional RG for the random field and random anisotropy O(N) sigma-models is studied to two loop. The ferromagnetic/disordered (F/D) transition fixed point is found to next order in d=4+epsilon for N > N_c (N_c=2.8347408 for random field, N_c=9.44121 for random anisotropy). For N < N_c the lower critical dimension plunges below d=4: we find two fixed points, one describing the quasi-ordered phase, the other is novel and describes the F/D transition. The lower critical dimension can be obtained in an (N_c-N)-expansion. The theory is also analyzed at large N and a glassy regime is found.

cond-mat.dis-nn↗

arXiv2005

Chaos and residual correlations in pinned disordered systems

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 $|x-x'|^{2 ζ- μ}$, the decorrelation exponent $μ$ proportional to the difference between Flory (or mean field) and exact roughness exponent $ζ$. For short range disorder $μ>0$ but small, e.g. for random bond interfaces $μ= 5 ζ- ε$, $ε=4-d$, and $μ= ε(\frac{(2 π)^2}{36} - 1)$ for the one component Bragg glass. Random field (i.e long range) disorder exhibits finite residual correlations (no chaos $μ= 0$) described by new FRG fixed points. Temperature and dynamic chaos (depinning) are discussed.

cond-mat.dis-nn↗

arXiv2005

2-loop Functional Renormalization for elastic manifolds pinned by disorder in N dimensions

We study elastic manifolds in a N-dimensional random potential using functional RG. We extend to N>1 our previous construction of a field theory renormalizable to two loops. For isotropic disorder with O(N) symmetry we obtain the fixed point and roughness exponent to next order in epsilon=4-d, where d is the internal dimension of the manifold. Extrapolation to the directed polymer limit d=1 allows some handle on the strong coupling phase of the equivalent N-dimensional KPZ growth equation, and eventually suggests an upper critical dimension of about 2.5.

cond-mat.dis-nn↗

arXiv2005

Functional Renormalization for pinned elastic systems away from their steady states

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 by a single dynamical exponent $z \approx c/T$, where $c$ compares well with recent numerical work. This agrees with the thermal boundary layer picture of pinned systems.

cond-mat.dis-nn↗

arXiv2004

Can non-linear elasticity explain contact-line roughness at depinning?

We examine whether cubic non-linearities, allowed by symmetry in the elastic energy of a contact line, may result in a different universality class at depinning. Standard linear elasticity predicts a roughness exponent zeta=1/3 (one loop), zeta=0.39 (numerics) while experiments give zeta of about 0.5. Within functional RG we find that a non-local KPZ-type term is generated at depinning and grows under coarse graining. A fixed point with zeta=0.45 (one loop) is identified, showing that large enough cubic terms increase the roughness. This fixed point is unstable, revealing a rough strong-coupling phase. Experimental study of contact angles theta near pi/2, where cubic terms vanish in the energy, is suggested.

cond-mat.soft↗

arXiv2004

Specific Heat of Quantum Elastic Systems Pinned by Disorder

We present the detailed study of the thermodynamics of vibrational modes in disordered elastic systems such as the Bragg glass phase of lattices pinned by quenched impurities. Our study and our results are valid within the (mean field) replica Gaussian variational method. We obtain an expression for the internal energy in the quantum regime as a function of the saddle point solution, which is then expanded in powers of $\hbar$ at low temperature $T$. In the calculation of the specific heat $C_v$ a non trivial cancellation of the term linear in $T$ occurs, explicitly checked to second order in $\hbar$. The final result is $C_v \propto T^3$ at low temperatures in dimension three and two. The prefactor is controlled by the pinning length. This result is discussed in connection with other analytical or numerical studies.

cond-mat.dis-nn↗