Smooth phases, roughening transitions, and novel exponents in one-dimensional growth models

@article{Alon1998SmoothPR,
  title={Smooth phases, roughening transitions, and novel exponents in one-dimensional growth models},
  author={Uri Alon and Martin R Evans and Haye Hinrichsen and David Mukamel},
  journal={Physical Review E},
  year={1998},
  volume={57},
  pages={4997-5012}
}
A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place in these models are related to contact processes or directed percolation type problems. The models are analyzed using a mean field approximation, scaling arguments and numerical simulations. In the smooth phase the symmetry of the underlying dynamics is… 
MEAN-FIELD CRITICAL BEHAVIOR AND ERGODICITY BREAK IN A NONEQUILIBRIUM ONE-DIMENSIONAL RSOS GROWTH MODEL
We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as
Stochastic processes and conformal invariance.
TLDR
It is shown that the probability distribution of the avalanche sizes obeys finite-size scaling with new critical exponents and implies in a rigorous way a connection between logarithmic conformal field theory and stochastic processes.
Non-equilibrium critical phenomena and phase transitions into absorbing states
This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed
The Raise and Peel Model of a Fluctuating Interface
We propose a one-dimensional nonlocal stochastic model of adsorption and desorption depending on one parameter, the adsorption rate. At a special value of this parameter, the model has some
Critical Phenomena in Nonequilibrium Systems
This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed
Logarithmic roughening in a growth process with edge evaporation.
  • H. Hinrichsen
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
TLDR
Performing high-precision simulations, this work finds appropriate scaling forms for various quantities in the roughening transition in a solid-on-solid growth process with edge evaporation and presents a simple approximation explaining why the interface roughens logarithmically.
Finite size effects in nonequilibrium wetting
Models with a nonequilibrium wetting transition display a transition also in finite systems. This is different from nonequilibrium phase transitions into an absorbing state, where the stationary
Mean-field approximations for the restricted solid-on-solid growth models
We study models for surface growth with a wetting and a roughening transition using simple and pair mean-field approximations. The simple mean-field equations are solved exactly and they predict the
Directed percolation with long-range interactions: Modeling nonequilibrium wetting.
TLDR
It is argued that some phase transitions observed in models of nonequilibrium wetting phenomena are related to contact processes with long-range interactions and belongs to the universality class of directed percolation.
Nonequilibrium wetting
When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied trough Langevin equations or
...
...

References

Lecture notes on particle systems and percolation
The simplest growth models. The voter model. The biased voter model. The contact process. One-dimensional discrete time models. Percolation in two dimensions. Mandelbrot's percolation process.