EXACT EXPONENT-LAMBDA OF THE AUTOCORRELATION FUNCTION FOR A SOLUBLE MODEL OF COARSENING

The exponent λ that describes the decay of the autocorrelation function A(t) in a phase ordering system, A(t)∼L-(d-λ), where d is the dimension and L the characteristic length scale at time t, is calculated exactly for the time-dependent Ginzburg-Landau equation in d=1. We find λ=0.3993835.... We also show explicitly that a small bias of positive domains over negative gives a magnetization which grows in time as M(t)∼Lμ and prove that for the one-dimensional Ginzburg-Landau equation, μ=λ, exemplifying a general result. © 1995 The American Physical Society.