Interplay of interfacial noise and curvature-driven dynamics in two dimensions

We explore the effect of interplay of interfacial noise and curvature-driven dynamics in a binary spin system. An appropriate model is the generalized two-dimensional voter model proposed earlier [M. J. de Oliveira, J. F. F. Mendes, and M. A. Santos, J. Phys. A: Math. Gen. 26, 2317 (1993)], where the flipping probability of a spin depends on the state of its neighbors and is given in terms of two parameters, x and y. x = 0.5 and y = 1 correspond to the conventional voter model which is purely interfacial noise driven, while x = 1 and y = 1 correspond to the Ising model, where coarsening is fully curvature driven. The coarsening phenomena for 0.5 < x < 1 keeping y = 1 is studied in detail. The dynamical behavior of the relevant quantities show characteristic differences from both x = 0.5 and 1. The most remarkable result is the existence of two time scales for x >= x(c) where x(c) approximate to 0.7. On the other hand, we have studied the exit probability which shows Ising-like behavior with a universal exponent for any value of x > 0.5; the effect of x appears in altering the value of the parameter occurring in the scaling function only.