NONTRIVIAL ALGEBRAIC DECAY IN A SOLUBLE MODEL OF COARSENING

A non-trivial exponent beta characterising non-equilibrium coarsening processes is calculated in a soluble model. For a spin model, the expo nent describes how the fraction p0 of spins which have never flipped ( or, equivalently, the fraction of space which has never been traversed by a domain wall) depends on the characteristic domain scale L: p0 is -similar-to L(beta-1). For the one-dimensional time-dependent Ginzburg -Landau equation at zero temperature we show that the critical exponen t beta is the zero of a transcendental equation, and find beta = 0.824 924 12....