Analytical Methods and Field Theory for Disordered Systems
arXiv:1705.07457
Abstract
This thesis presents several aspects of the physics of disordered elastic systems and of the analytical methods used for their study. On one hand we will be interested in universal properties of avalanche processes in the statics and dynamics (at the depinning transition) of elastic interfaces of arbitrary dimension in disordered media at zero temperature. To study these questions we will use the functional renormalization group. After a review of these aspects we will more particularly present the results obtained during the thesis on (i) the spatial structure of avalanches and (ii) the correlations between avalanches. On the other hand we will be interested in static properties of directed polymers in dimension, and in particular in observables related to the KPZ universality class. In this context the study of exactly solvable models has recently led to important progress. After a review of these aspects we will be more particularly interested in exactly solvable models of directed polymer on the square lattice and present the results obtained during the thesis in this direction: (i) classification of Bethe ansatz exactly solvable models of directed polymer at finite temperature on the square lattice; (ii) KPZ universality for the Log-Gamma and Inverse-Beta models; (iii) KPZ universality and non-universality for the Beta model; (iv) stationary measures of the Inverse-Beta model and of related zero temperature models.
PhD Thesis. 172+18pages
References in corpus (97)
- Crackling Noise
- The Exact Renormalisation Group and Approximate Solutions
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Creep and depinning in disordered media
- Collective Transport: From Superconductors to Earthquakes
- Discrete polynuclear growth and determinantal processes
- Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
- Burgers Turbulence
- Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
- Free-energy distribution of the directed polymer at high temperature
- Level-Spacing Distributions and the Airy Kernel
- Growing interfaces uncover universal fluctuations behind scale invariance
- Scaling description of the yielding transition in soft amorphous solids at zero temperature
- Asymptotics in ASEP with Step Initial Condition
- On the Numerical Evaluation of Fredholm Determinants
- Statistics of Earthquakes in Simple Models of Heterogeneous Faults
- Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach
- Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
- Exact Solution of the Master Equation for the Asymmetric Exclusion Process
- Beyond power laws: Universality in the average avalanche shape
- Scaling exponents for Barkhausen avalanches in polycrystals and amorphous ferromagnets
- A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
- An exact solution for the KPZ equation with flat initial conditions
- Scaling for a one-dimensional directed polymer with boundary conditions
- The one-dimensional KPZ equation and its universality class
- Renormalization of pinned elastic systems: how does it work beyond one loop ?
- Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
- Exact height distributions for the KPZ equation with narrow wedge initial condition
- Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
- Transport in Sand Piles, Interface Depinning, and Earthquake Models
- Quasi-static crack propagation in heterogeneous media
- Driven Interface Depinning in a Disordered Medium
- Signature of effective mass in crackling noise asymmetry
- Exact solution for the stationary Kardar-Parisi-Zhang equation
- The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1
- A Fredholm Determinant Representation in ASEP
- Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
- The KPZ equation with flat initial condition and the directed polymer with one free end
- Avalanche-size distribution at the depinning transition: A numerical test of the theory
- Avalanches and clusters in planar crack front propagation
- Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
- Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of records
- Log-Gamma polymer free energy fluctuations via a Fredholm determinant identity
- Random-walk in Beta-distributed random environment
- Size distributions of shocks and static avalanches from the Functional Renormalization Group
- Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
- Kinetic Roughening in Slow Combustion of Paper
- Stationary correlations for the 1D KPZ equation
- Viscoelastic Effects in Avalanche Dynamics: A Key to Earthquake Statistics
- Creep motion of an elastic string in a random potential
- Renormalization fixed point of the KPZ universality class
- Probability distribution of the free energy of a directed polymer in a random medium
- The Large Scale Energy Landscapes of Randomly Pinned Objects
- Statistics of static avalanches in a random pinning landscape
- Directed polymer near a hard wall and KPZ equation in the half-space
- Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study
- Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition
- Universal fluctuations and extreme statistics of avalanches near the depinning transtition
- Fracture Roughness Scaling: a case study on planar cracks
- The average shape of a fluctuation: universality in excursions of stochastic processes
- Creep via dynamical functional renormalization group
- Avalanche dynamics of elastic interfaces
- Crossover from Growing to Stationary Interfaces in the Kardar-Parisi-Zhang Class
- An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media
- Quantitative scaling of magnetic avalanches
- Measuring functional renormalization group fixed-point functions for pinned manifolds
- Avalanches and Correlations in Driven Interface Depinning
- The One-dimensional KPZ Equation and the Airy Process
- The strict-weak lattice polymer
- First-principle derivation of static avalanche-size distribution
- Distribution of velocities in an avalanche
- Experimental approaches to universal out-of-equilibrium scaling laws: turbulent liquid crystal and other developments
- On Time Correlations for KPZ Growth in One Dimension
- Large deviation rate functions for the partition function in a log-gamma distributed random potential
- Two-point free energy distribution function in (1+1) directed polymers
- Ground state energy of a non-integer number of particles with delta attractive interactions
- Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics
- Exact renormalization group and applications to disordered problems: part I
- Short time growth of a KPZ interface with flat initial conditions
- Statics and dynamics of elastic manifolds in media with long-range correlated disorder
- Statistics of Avalanches with Relaxation, and Barkhausen Noise: A Solvable Model
- Distribution of maximum velocities in avalanches near the depinning transition
- Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems
- Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
- Shape of a Barkhausen pulse
- Aftershock production rate of driven viscoelastic interfaces
- Revisiting Directed Polymers with heavy-tailed disorder
- The universal high temperature regime of pinned elastic objects
- Driven interfaces: from flow to creep through model reduction
- Spatial shape of avalanches in the Brownian force model
- Distribution of joint local and total size and of extension for avalanches in the Brownian force model
- Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
- On two-time distribution functions in (1+1) random directed polymers
- Universal correlations between shocks in the ground state of elastic interfaces in disordered media
- Universality for directed polymers in thin rectangles
- Universality in the mean spatial shape of avalanches
- Scaling theory of thermal rounding phenomena in depinning and related transitions