Directed d -mer diffusion describing the Kardar-Parisi-Zhang-type surface growth

G. Ódor, Bartosz Liedke, Karl Heinz Heinig

Research output: Article

25 Citations (Scopus)

Abstract

We show that d+1 -dimensional surface growth models can be mapped onto driven lattice gases of d -mers. The continuous surface growth corresponds to one dimensional drift of d -mers perpendicular to the (d-1) -dimensional "plane" spanned by the d -mers. This facilitates efficient bit-coded algorithms with generalized Kawasaki dynamics of spins. Our simulations in d=2, 3, 4, 5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far, where the effective growth exponent exhibits an increase. We provide evidence for the agreement with field theoretical predictions of the Kardar-Parisi-Zhang universality class and numerical results. We show that the (2+1) -dimensional exponents conciliate with the values suggested by Lässig within error margin, for the largest system sizes studied here, but we cannot support his predictions for (3+1) d numerically.

Original languageEnglish
Article number031112
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume81
Issue number3
DOIs
Publication statusPublished - márc. 12 2010

Fingerprint

Surface Growth
Exponent
Kawasaki Dynamics
exponents
Lattice Gas
Prediction
Scaling Exponent
Growth Model
Margin
Perpendicular
Universality
Simulation
predictions
Numerical Results
margins
simulation
Estimate
scaling
estimates
gases

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Directed d -mer diffusion describing the Kardar-Parisi-Zhang-type surface growth. / Ódor, G.; Liedke, Bartosz; Heinig, Karl Heinz.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 81, No. 3, 031112, 12.03.2010.

Research output: Article

@article{b0ad0f35b2b14b1cbe82fa9c6a5d7e7d,
title = "Directed d -mer diffusion describing the Kardar-Parisi-Zhang-type surface growth",
abstract = "We show that d+1 -dimensional surface growth models can be mapped onto driven lattice gases of d -mers. The continuous surface growth corresponds to one dimensional drift of d -mers perpendicular to the (d-1) -dimensional {"}plane{"} spanned by the d -mers. This facilitates efficient bit-coded algorithms with generalized Kawasaki dynamics of spins. Our simulations in d=2, 3, 4, 5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far, where the effective growth exponent exhibits an increase. We provide evidence for the agreement with field theoretical predictions of the Kardar-Parisi-Zhang universality class and numerical results. We show that the (2+1) -dimensional exponents conciliate with the values suggested by L{\"a}ssig within error margin, for the largest system sizes studied here, but we cannot support his predictions for (3+1) d numerically.",
author = "G. {\'O}dor and Bartosz Liedke and Heinig, {Karl Heinz}",
year = "2010",
month = "3",
day = "12",
doi = "10.1103/PhysRevE.81.031112",
language = "English",
volume = "81",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Directed d -mer diffusion describing the Kardar-Parisi-Zhang-type surface growth

AU - Ódor, G.

AU - Liedke, Bartosz

AU - Heinig, Karl Heinz

PY - 2010/3/12

Y1 - 2010/3/12

N2 - We show that d+1 -dimensional surface growth models can be mapped onto driven lattice gases of d -mers. The continuous surface growth corresponds to one dimensional drift of d -mers perpendicular to the (d-1) -dimensional "plane" spanned by the d -mers. This facilitates efficient bit-coded algorithms with generalized Kawasaki dynamics of spins. Our simulations in d=2, 3, 4, 5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far, where the effective growth exponent exhibits an increase. We provide evidence for the agreement with field theoretical predictions of the Kardar-Parisi-Zhang universality class and numerical results. We show that the (2+1) -dimensional exponents conciliate with the values suggested by Lässig within error margin, for the largest system sizes studied here, but we cannot support his predictions for (3+1) d numerically.

AB - We show that d+1 -dimensional surface growth models can be mapped onto driven lattice gases of d -mers. The continuous surface growth corresponds to one dimensional drift of d -mers perpendicular to the (d-1) -dimensional "plane" spanned by the d -mers. This facilitates efficient bit-coded algorithms with generalized Kawasaki dynamics of spins. Our simulations in d=2, 3, 4, 5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far, where the effective growth exponent exhibits an increase. We provide evidence for the agreement with field theoretical predictions of the Kardar-Parisi-Zhang universality class and numerical results. We show that the (2+1) -dimensional exponents conciliate with the values suggested by Lässig within error margin, for the largest system sizes studied here, but we cannot support his predictions for (3+1) d numerically.

UR - http://www.scopus.com/inward/record.url?scp=77949369432&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949369432&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.81.031112

DO - 10.1103/PhysRevE.81.031112

M3 - Article

VL - 81

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 3

M1 - 031112

ER -