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Generalizations of the KPZ equation (minor changes to enable easy latexing)

J. P. Doherty·M. A. Moore·J. M. Kim·A. J. Bray
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Abstract

We generalize the KPZ equation to an O(3) $N=2j+1$ component model. In the limit $N \to \infty$ we show that the mode coupling equations become exact. Solving these approximately we find that the dynamic exponent $z$ increases from $3/2$ for $d=1$ to $2$ at the dimension $d\approx3.6$. For $d=1$ it can be shown analytically that $z=3/2$ for all $j$. The case $j=2$ for $d=2$ is investigated by numerical integration of the KPZ equation.

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J. P. Doherty, M. A. Moore, J. M. Kim, A. J. Bray. 1993-07-30. Generalizations of the KPZ equation (minor changes to enable easy latexing). https://arxiv.org/abs/cond-mat/9307053

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