Phase-ordering dynamics with an order-parameter-dependent mobility: The large- n limit

The effect of an order-parameter-dependent mobility (or kinetic coefficient), given by ${λ}({{→}}{{φ}}){∝}(1{-}{{{→}}{{φ}}}²{)}^{{α}},$ on the phase-ordering dynamics of a system described by an n-component vector order parameter is addressed at zero temperature in the large-n limit. In this limit the system is exactly soluble for both conserved and nonconserved order parameter; in the nonconserved case the scaling form for the correlation function and its Fourier transform, the structure factor, is established, with the characteristic length growing as L~t^1/2(1+α). In the conserved case, the structure factor is evaluated and found to exhibit a multiscaling behavior, with two growing length scales differing by a logarithmic factor: L₁~t^1/2(2+α) and L₂~(t/lnt)^1/2(2+α).