Effect of Long-Range Interactions in the Conserved Kardar-Parisi-Zhang   Equation
  The conserved Kardar-Parisi-Zhang equation in the presence of long-range nonlinear interactions is studied by the dynamic renormalization group method. The long-range effect produces new fixed points with continuously varying exponents and gives distinct phase transitions, depending on both the long-range interaction strength and the substrate dimension $d$. The long-range interaction makes the surface width less rough than that of the short-range interaction. In particular, the surface becomes a smooth one with a negative roughness exponent at the physical dimension d=2. 
Youngkyun Jung, In-mook Kim (Korea Univ.), and Jin Min Kim(Soongsil   Univ.)