Anomalous fluctuations of directed polymers in random media.

A systematic analysis of large-scale fluctuations in the low-temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ground states.'' The probability distribution of their sizes is found to have a power-law tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the mapping to the noisy Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet excitations and a recent variational approach with broken replica symmetry.'' It is argued that the power-law distribution of large thermally active excitations is a consequence of the continuous statistical tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.

• Publication year

  1993

• Venue

  Physical Review B (Condensed Matter)

• Publication date

  1993-09-14

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PhysRevB.49.3136arXiv cond-mat/9309016PMID 10011171
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Self-consistent approach to the Kardar-Parisi-Zhang equation.

  1993cited by this paper
• Threshold critical dynamics of driven interfaces in random media.

  1993cited by this paper
• Large-N expansion of (4- epsilon )-dimensional oriented manifolds in random media.

  1993cited by this paper
• Nonequilibrium dynamics of driven line liquids.

  1992cited by this paper
• Variational theory for the pinning of vortex lattices by impurities.

  1992cited by this paper
• Exact dynamical exponent at the Kardar-Parisi-Zhang roughening transition.

  1992cited by this paper
• Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes.

  1992cited by this paper
• Directed polymers in random media: Probability distributions.

  1991cited by this paper
• Variational theory for disordered vortex lattices.

  1991cited by this paper
• Exact scaling function of interface growth dynamics.

  1991cited by this paper
• School of Natural Sciences, Institute for Advanced Study,

  1991cited by this paper
• Zero-temperature directed polymers in a random potential.

  1991cited by this paper
• Directed paths in a random potential.

  1991cited by this paper
• Theory of collective flux creep.

  1989cited by this paper
• Scaling and universality in avalanches.

  1989cited by this paper
• Burgers equation with correlated noise: Renormalization-group analysis and applications to directed polymers and interface growth.

  1989cited by this paper
• Self-organized criticality.

  1988cited by this paper
• Nonequilibrium dynamics of spin glasses.

  1988cited by this paper
• Equilibrium behavior of the spin-glass ordered phase.

  1988cited by this paper
• Mechanism for superuniversal behavior in certain stochastic systems.

  1988cited by this paper
• Ground state instability of a random system.

  1987cited by this paper
• Self-organized criticality: An explanation of the 1/f noise.

  1987cited by this paper
• Scaling of directed polymers in random media.

  1987cited by this paper
• Spin Glass Theory and Beyond

  1987cited by this paper
• Dynamic scaling of growing interfaces.

  1986cited by this paper
• Interface fluctuations in disordered systems: 5- epsilon expansion and failure of dimensional reduction.

  1986cited by this paper
• Huse, Henley, and Fisher respond.

  1985cited by this paper
• Pinning and roughening of domain walls in Ising systems due to random impurities.

  1985cited by this paper
• Excess noise for driven diffusive systems.

  1985cited by this paper
• Field Theory, the Renormalization Group and Critical Phenomena

  1984cited by this paper
• Field theory

  1979influential reference

• Hyperuniformity at the Absorbing State Transition: Perturbative RG for Random Organization

  2025cites this paper
• Localization length of the $1+1$ continuum directed random polymer

  2022cites this paper
• On end-point distribution for directed polymers and related problems for randomly forced Burgers equation

  2022cites this paper
• Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles

  2021cites this paper
• Benchmarking the nonperturbative functional renormalization group approach on the random elastic manifold model in and out of equilibrium

  2019cites this paper
• Darcy's Law for Yield Stress Fluids.

  2018cites this paper
• Field theory of disordered elastic interfaces at 3-loop order: Critical exponents and scaling functions

  2017cites this paper
• Phase Transitions and Scaling in Systems Far From Equilibrium

  2016cites this paper
• Persistence-length renormalization of polymers in a crowded environment of hard disks.

  2014cites this paper
• Replica Symmetry Breaking in Trajectories of a Driven Brownian Particle.

  2014cites this paper
• Static fluctuations of a thick one-dimensional interface in the 1+1 directed polymer formulation: numerical study.

  2013cites this paper
• Statistics of shocks in a toy model with heavy tails.

  2013cites this paper
• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium

  2013influential citation
• Static fluctuations of a thick one-dimensional interface in the 1+1 directed polymer formulation.

  2012cites this paper
• Finite-temperature and finite-time scaling of the directed polymer free energy with respect to its geometrical fluctuations.

  2012cites this paper
• Magnetoresistance of an Anderson insulator of bosons.

  2012cites this paper
• Theoretical studies of the interplay between superconductivity and disorder

  2012cites this paper
• Disordered elastic systems and one-dimensional interfaces

  2011cites this paper
• Random field Ising model: statistical properties of low-energy excitations and equilibrium avalanches

  2011cites this paper
• Exact results and open questions in first principle functional RG

  2008cites this paper
• Driven interfaces in random media at finite temperature: existence of an anomalous zero-velocity phase at small external force.

  2008cites this paper
• Chaos, concentration, and multiple valleys

  2008cites this paper
• Non-equilibrium dynamics of disordered systems: understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space

  2008cites this paper
• Polymers in Disordered Media

  2007cites this paper
• Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low temperature phase

  2007cites this paper
• Unzipping vortices in type-II superconductors

  2007cites this paper
• Statistics of low energy excitations for the directed polymer in a random medium.

  2006cites this paper
• Freezing transition of the directed polymer in a 1 + d random medium: location of the critical temperature and unusual critical properties.

  2006cites this paper
• Stepwise responses in mesoscopic glassy systems: A mean-field approach

  2006cites this paper
• Numerical study of the directed polymer in a 1 + 3 dimensional random medium

  2006cites this paper
• Mean-field limit of systems with multiplicative noise.

  2005cites this paper
• Variable-range cotunneling and conductivity of a granular metal

  2005cites this paper
• Nonequilibrium relaxation of an elastic string in a random potential.

  2005cites this paper
• Single-vortex fluctuations in layered superconductors: Electromagnetic coupling and crossover to strong pinning

  2004cites this paper
• Lindemann criterion and vortex lattice phase transitions in type-II superconductors

  2004cites this paper
• Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets

  2004cites this paper
• Low-temperature properties of some disordered systems from the statistical properties of nearly degenerate two-level excitations

  2004cites this paper
• Directed polymers and interfaces in random media: free-energy optimization via confinement in a wandering tube.

  2003cites this paper
• Functional renormalization group and the field theory of disordered elastic systems.

  2003cites this paper
• Broad relaxation spectrum and the field theory of glassy dynamics for pinned elastic systems.

  2003cites this paper
• Exact multilocal renormalization of the effective action: application to the random sine Gordon model statics and nonequilibrium dynamics.

  2003cites this paper
• Functional Renormalization Group at Large N for Disordered Elastic Systems, and Relation to Replica Symmetry Breaking

  2003cites this paper
• Fluctuations of the winding number of a directed polymer in a random medium.

  2003cites this paper
• Exact solutions for the statistics of extrema of some random 1D landscapes, application to the equilibrium and the dynamics of the toy model

  2002cites this paper
• Two-loop functional renormalization group theory of the depinning transition

  2002cites this paper
• Last Branching in Directed Last Passage Percolation

  2002cites this paper
• Fragility of the free-energy landscape of a directed polymer in random media.

  2002cites this paper
• Exact combinatorial algorithms: Ground states of disordered systems

  2001cites this paper
• Statistical mechanics of secondary structures formed by random RNA sequences.

  2001cites this paper
• Single molecule statistics and the polynucleotide unzipping transition.

  2001cites this paper
• Extremal statistics in the energetics of domain walls.

  2001cites this paper
• Proliferation assisted transport in a random environment

  2001cites this paper
• Ground-States of Two Directed Polymers

  2000cites this paper
• Energy landscapes in random systems, driven interfaces, and wetting

  2000cites this paper
• Exact multilocal renormalization group and applications to disordered problems.

  2000cites this paper
• Universal susceptibility variations in 1+1 dimensional vortex glass

  1999cites this paper
• Infinite moments of the partition function for random walks in a random potential

  1998cites this paper
• Scaling Laws and Similarity Detection in Sequence Alignment with Gaps

  1998cites this paper
• On growth, disorder, and field theory

  1998cites this paper
• On the long times, large length scale behaviour of disordered systems

  1997cites this paper
• Optimal detection of sequence similarity by local alignment

  1997cites this paper
• Origins of scale invariance in growth processes

  1997cites this paper
• Burgers’ turbulence and dynamical scaling

  1997cites this paper
• Directed polymers in a random environment: Some results on fluctuations

  1997cites this paper
• DNA sequence alignment and critical phenomena

  1996cites this paper
• Directed lines in sparse potentials

  1996cites this paper
• Mode-coupling and renormalization group results for the noisy Burgers equation.

  1996cites this paper
• A continuous time version of random walks in a random potential

  1996cites this paper
• Infinite number of exponents for a spin-glass transition.

  1996cites this paper
• Numerical results for the ground-state interface in a random medium.

  1995cites this paper
• Scaling of energy barriers for flux lines and other random systems.

  1995cites this paper
• Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles.

  1995cites this paper
• Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

  1995cites this paper
• Interacting flux lines in a random medium.

  1995cites this paper
• Statistical physics of growth processes

  1995cites this paper
• Off-equilibrium dynamics of a (1 + 1)-dimensional directed polymer in random media

  1995cites this paper
• Energy barriers to motion of flux lines in random media.

  1995cites this paper
• Large time out-of-equilibrium dynamics of a manifold in a random potential.

  1995cites this paper
• Ward identities for surface-growth models with diffusion.

  1994cites this paper
• Depinning in a Random Medium

  1994cites this paper
• Disorder-induced depinning transition.

  1994cites this paper