Self-consistent calculation of statics and dynamics of the roughening transition |
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Authors: | Yukio Saito |
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Institution: | (1) Institut für Festkörperforschung, Kernforschungsanlage Jülich GmbH, Postfach 1913, D-5170 Jülich 1, Federal Republic of Germany |
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Abstract: | Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT
R
is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h
2 are found to behave—lnF ln![xgr](/content/g6816166h356417w/xxlarge958.gif) ![sim](/content/g6816166h356417w/xxlarge8764.gif) h
2![rang](/content/g6816166h356417w/xxlarge9002.gif) (T
R
–T)–1 for temperaturesT approachingT
R
from below. The linear relaxation rate of the order parameter is found to be proportional to
–2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference![Delta](/content/g6816166h356417w/xxlarge916.gif) aboveT
R
, shows a metastable regime belowT
R
with a spinodal limit of metastability![Delta](/content/g6816166h356417w/xxlarge916.gif)
c
, beyond which oscillatory growth starts. The critical behavior of![Delta](/content/g6816166h356417w/xxlarge916.gif)
c
is found to be ln![Delta](/content/g6816166h356417w/xxlarge916.gif)
c
–(T
R
–T)–1+O(ln (T
R
–T)). |
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Keywords: | |
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