Growth of Long-Range Correlations after a Quench in Conserved-Order- Parameter Systems

We develop a general Langevin formalism for the dynamics after a quench to a critical point or an ordered phase, and use this to study a few specific cases. We present a general argument that for d spatial dimensions and conserved order parameter, the local autocorrelations decay as φ(r,0)φ(r,t) ∼L-d(t), where L(t) is the correlation length at time t, and φ is the order parameter. We also present new analytical and numerical results for the coarsening process after a quench to zero temperature in the ferromagnetic Ising chain with conserved magnetization.