Late-time theory for the effects of a conserved field on the kinetics of an order-disorder transition

The dynamics of an order-disorder transition is investigated through a nonlinear Langevin model known as model C. This model describes the dynamics of an ordering nonconserved field (e.g., sublattice concentration), _, coupled to a nonordering conserved field (e.g., absolute concentration), c. An approximate asymptotic time-dependent solution is presented for both fields through a singular perturbative solution of the coupled nonlinear-dynamical system. In particular, analytic expressions for the dynamic structure factors [i.e., S_(k,t)==__(k,t)_*(k,t)_, and Sc(k,t)==_c(k,t)c*(k,t)_, where k is the wave vector and t is time] of both fields are presented. In the late-time regime these expressions reduce to the scaling forms S_(k,t)_td/2f_(Q) and Sc(k,t)_td/2-1fc(Q), where Q=kt1/2. Furthermore it is shown that f_(Q)_Q-d-1, fc(Q)_Q-d+1 for Q_1 and fc(Q)_Q4 for Q_1. Intermediate-time corrections, due to a finite interfacial width, to the asymptotic solutions of both fields are also obtained. Many of these predictions are experimentally accessible