Finite-size effects on critical diffusion and relaxation towards metastable equilibrium

We present an analytic study of finite-size effects on critical diffusion above and below Tc of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size relaxation time that governs the critical order-parameter relaxation towards a metastable equilibrium state below Tc. Two universal dynamic amplitude ratios at Tc are predicted and quantitative predictions of dynamic finite-size scaling functions are given that can be tested by Monte Carlo simulations.