Kardar-Parisi-Zhang Equation And Its Critical Exponents Through Local Slope-Like Fluctuations

Growth of interfaces during vapor deposition are analyzed on a discrete lattice. Foe a rough surface, relation between the roughness exponent alpha, and corresponding step-step (slope-slope) couplings is obtained in (1+1) and (2+1) dimensions. From the discrete form and the symmetries of the growth problem, the step -step couplings can be determined. Thus alpha can be obtained. The method is applied to Edward-Wilkinson type and Kardar- Parisi -Zhang equations in all the dimensions to obtain exact values of alpha. It is further applied to the fourth order linear and non linear terms. Exact values of roughness coefficients in these cases are obtained. The method is thus applicable to any linear or nonlinear stochastic equation with non conserved noise for obtaining the exact asymptoic exponents.