THEORY OF PHASE ORDERING KINETICS

The theory of phase ordering kinetics is reviewed, and new results for systems with continuous symmetry presented. A generalisation of ''Porod's law'' for the tail of the structure factor, of the form S(k, t) approximately k-(d+n)L(t)-n for kL(t) much greater than 1, where L(t) is the characteristic length scale at time t after the quench, is derived where, for a vector order parameter, n is simply the number of components of the vector. The power-law tail is shown to be associated with topological defects in the field, and its amplitude is calculated exactly in terms of the defect density. For a conserved vector order parameter the multiscaling form obtained for n = infinity is argued to be special to this limit. Using an approximate theory due to Mazenko, it is shown that conventional scaling is recovered. for any finite n, when t --> infinity, with L(t) approximately (t/ln n)1/4 for n large.