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We present a formalism to derive the stochastic differential equations (SDEs)for several solid-on-solid growth models. Our formalism begins with a mappingof the microscopic dynamics of growth models onto the particle systems withreactions and diffusion. We then write the master equations for thesecorresponding particle systems and find the SDEs for the particle densities.Finally, by connecting the particle densities with the growth heights, wederive the SDEs for the height variables. Applying this formalism to discretegrowth models, we find the Edwards-Wilkinson equation for the symmetricbody-centered solid-on-solid (BCSOS) model, the Kardar-Parisi-Zhang equationfor the asymmetric BCSOS model and the generalized restricted solid-on-solid(RSOS) model, and the Villain--Lai--Das Sarma equation for the conserved RSOSmodel. In addition to the consistent forms of equations for growth models, wealso obtain the coefficients associated with the SDEs.Comment: 5 pages, no figur

Derivation of continuum stochastic equations for discrete growth models