Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

  title={Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics},
  author={Timothy Halpin-Healy and Yicheng Zhang},
  journal={Physics Reports},
Stochastic Surface Growth
Growth phenomena constitute an important field in nonequilibrium statistical mechanics. Kardar, Parisi, and Zhang (KPZ) in 1986 proposed a continuum theory for local stochastic growth predicting
Multi-facets of kinetic roughening of interfaces
Abstract In this review, the authors are going to explore the intriguing aspects of kinetic roughening of interfaces. Interface roughness dynamics connected with various physical processes have been
Growing interfaces uncover universal fluctuations behind scale invariance
This work investigates growing interfaces of liquid-crystal turbulence and finds not only universal scaling, but universal distributions of interface positions, which obey the largest-eigenvalue distributions of random matrices and depend on whether the interface is curved or flat, albeit universal in each case.
Origins of scale invariance in growth processes
Abstract This review describes recent progress in the understanding of the emergence of scale invariance in far-from-equilibrium growth. The first section is devoted to ‘solvable’ needle models which
Statistical physics of growth processes
The topic of these lectures is the formation of scale invariant structures through far-from-equilibrium growth processes. This class of problems entered into the realm of statistical physics with the
Macroscopic order from reversible and stochastic lattice growth models
This thesis advances the understanding of how autonomous microscopic physical processes give rise to macroscopic structure. A unifying theme is the use of physically motivated microscopic models of
Random interface growth in a random environment: Renormalization group analysis of a simple model
We study the effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modeled by the well-known
Universal Behavior of Driven Diffusive Lattice Gases
This cumulative dissertation is dedicated to the study of universal behavior in one-dimensional driven diffusive systems far from equilibrium. To capture essential aspects of such systems we will
Analytical Methods and Field Theory for Disordered Systems
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
An invariance principle for the 1D KPZ equation
A BSTRACT . Consider a discrete one-dimensional random surface whose height at a point grows as a function of the heights at neighboring points plus an independent random noise. Assuming that this


On the kinetic roughening of vicinal surfaces.
This work has performed extensive numerical simulations of this stochastic partial differential equation in an attempt to investigate Wolf's claim of logarithmic, rather than algebraic, roughness, complementing the evidence provided by simulations of various microscopic growth models.
Amplitude universality for driven interfaces and directed polymers in random media.
We present accurate estimates for the prefactors of the second and third moments of the height and free-energy fluctuations, as well as the leading correction to the growth rate and free energy per
Non-directed polymers in a random medium
We study an ensemble of polymers that strongly interact with the surrounding medium. One end of the polymers is fixed. but otherwise there are no restrictions on their possible Conformations,
Directed polymers in the presence of colununar disorder
We consider directed polymers in a random landscape that is completely correlated in the time direction. This problem is closely related to diffusion-reproduction processes and undirected Gaussian
Anomalous fluctuations of directed polymers in random media.
  • HwaFisher
  • Physics
    Physical review. B, Condensed matter
  • 1994
It is argued that the power-law distribution of large thermally active excitation 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.
Burgers equation with correlated noise: Renormalization-group analysis and applications to directed polymers and interface growth.
The Burgers equation is the simplest nonlinear generalization of the diffusion equation subject to random noise and it is shown that an exponent identity observed in all simulations so far follows simply from the Galilean invariance of the equation in the absence of temporal correlations.
Large-distance and long-time properties of a randomly stirred fluid
Dynamic renormalization-group methods are used to study the large-distance, long-time behavior of velocity correlations generated by the Navier-Stokes equations for a randomly stirred, incompressible
This paper reviews simulational and theoretical investigations of critical behavior in a stochastic, interacting lattice gas under the influence of a uniform external driving field. By studying this
On the glassy nature of random directed polymers in two dimensions
We study numerically directed polymers in a random potential in 1 + 1 dimensions. We introduce two copies of the polymer, coupled through a thermodynamic local interaction. We show that the system is