Ward identities for surface-growth models with diffusion.

Abstract

Using the method of Hwa and Fisher [Phys. Rev. B 49, 3136 (1994)], we derive Ward identities relating the two- and three-point vertex functions in the dynamic functional theory for surface-growth models with diffusion. These identities result from the statistical transformation symmetries in the underlying Langevin equations for these models. An explicit scaling form for the full three-point vertex function is also obtained. As a result one can show that the scaling properties of the full three-point vertex function are the same as those of the ``bare'' vertex function obtained in the case of no stochastic noise. This implies that the coupling constant for the nonlinear term in the Langevin equation is not renormalized.