Explicit dynamic finite-size scaling in the time-dependent correlation functions for the two-dimensional classical XY model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time scaling variables of the model. It shows nontrivial dynamic finite-size scaling behavior near and below TKT for the total spin correlation function. Since the model is critical for all temperatures below TKT, the time scaling exponent is markedly different from that of the three-dimensional classical XY model at short times. There also appears to be another dynamic scaling region with a different time scaling exponent at T⩽TKT for a fairly wide intermediate time interval.
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.