Systematic deviation from scaling in the dynamics of a random interface: Case for a nonzero initial order parameter

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Abstract
We investigate the dynamic behavior of a system quenched far below the order-disorder transition temperature. The system with which we are concerned consists of random interfaces between two stable phases and initially takes finite values for both the order parameter and the area density of interfaces. We apply extensively the theory, named u-field theory, by Ohta, Jasnow, and Kawasaki [Phys. Rev. Lett. 49, 1223 (1982)] to this system. It is found that, in the case of a finite initial order parameter, the area density shows an exponential decay with time. The time dependence of the order parameter can be represented by a universal function without respect to the initial conditions. These theoretical predictions are justified via a Monte Carlo simulation of a spin-flip kinetic Ising model.