Anomaly of the height-height correlation functions in self-flattening surface growth

By Monte Carlo simulations and scaling theories, we consider the height-height correlation function G(r,t;L) of the one-dimensional equilibrium self-flattening surface growths, where the deposition (evaporation) attempt only at the globally highest (lowest) site is suppressed. G(r,t:L) is shown to satisfy the anomalous scaling behavior G(r,t;L)=L(2alpha)g(1)(r/L(delta),t/L(z)) or G(r,t;L)=t(2beta)g(2)(r/t(1/z(')),L/t(1/z)). Here alpha, beta, and z are the roughness, growth, and dynamic exponents, respectively, for the surface width, with alpha=1/3 and z=alpha/beta=3/2. Anomalous exponents z(') and delta are found to satisfy z(')=9/4 and delta=z/z('). We also show that anomalous behavior of G(r,t;L) can be understood from a scaling theory based on the competition between local random-walk-like behavior and the global-length-scale suppression.