GENERALIZATIONS OF THE KARDAR-PARISI-ZHANG EQUATION

We generalize the Kardar-Parisi-Zhang (KPZ) equation to an O(3) N = 2j + 1 component model. In the limit N --> infinity 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 almost-equal-to 3.6. 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.