PMID: 11308688Apr 20, 2001Paper

Nonequilibrium roughening transition in a volume conserving system

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
K ParkI Kim

Abstract

We introduce a simple volume conserving stochastic model undergoing a nonequilibrium roughening transition (NRT) in 1+1 dimensions. In our model, there is no deposition and evaporation of a particle breaking the volume conserving condition. The degree of roughness of the fluctuating interface in our model is determined by whether or not the hopping of a particle depends on the local slope of the interface. The hopping process of a particle is controlled by the probability 0<or=p<or=1. For p<1/2, a moving particle tends to hop in the downhill direction of the local slope of the interface, and so the interface is in a smooth phase with a zero roughness exponent. For p>1/2, a particle tends to hop in the uphill direction, and so the interface cannot reach a saturated phase. When p=1/2, the hopping of a particle does not depend on the local slope of the interface. Then the interface can reach a saturated phase. The saturated interface at p=1/2 is in a rough phase with a nonzero roughness exponent. Our model, therefore, exhibits the NRT at the critical parameter p(c)=1/2.

References

Nov 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·H Park, M H Kim
Dec 2, 1985·Physical Review Letters·R Savit, R Ziff
May 29, 1989·Physical Review Letters·J Kertész, D E Wolf
May 18, 1992·Physical Review Letters·H Takayasu, A Y Tretyakov
Nov 7, 1994·Physical Review Letters·M H Kim, H Park
Apr 8, 1996·Physical Review Letters·U AlonD Mukamel
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·K Park, I m Kim
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y Jung, I M Kim Im

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