Order-parameter relaxation times of finite three-dimensional Ising-like systems

We present field-theoretic and numerical studies of finite-size effects on the exponential relaxation times tau(1) and tau(2) of the order parameter and the square of the order parameter near the critical point of three-dimensional Ising-like systems. Finite-size scaling functions of tau(1) and tau(2) are calculated for the relaxational dynamics of the phi(4) model in cubic geometry with periodic boundary conditions. At T-c we predict the universal ratio tau(1)/tau(2) = 5.4. Below T-c, a maximum of tau(2) is predicted. New Monte Carlo data for the Ising model are presented which are in good agreement with the predictions.