  We study how the finite-sized n-component model A with periodic boundary
conditions relaxes near its bulk critical point from an initial nonequilibrium
state with short-range correlations. Particular attention is paid to the
universal long-time traces that the initial condition leaves. An approach based
on renormalization-group improved perturbation theory in 4-epsilon space
dimensions and a nonperturbative treatment of the q=0 mode of the fluctuating
order-parameter field is developed. This leads to a renormalized effective
stochastic equation for this mode in the background of the other q=0 modes; we
explicitly derive it to one-loop order, show that it takes the expected
finite-size scaling form at the fixed point, and solve it numerically. Our
results confirm for general n that the amplitude of the magnetization density
m(t) in the linear relaxation-time regime depends on the initial magnetization
in the universal fashion originally found in our large-$n$ analysis [J.\ Stat.
Phys. 73 (1993) 1]. The anomalous short-time power-law increase of m(t) also is
recovered. For n=1, our results are in fair agreement with recent Monte Carlo
simulations by Li, Ritschel, and Zheng [J. Phys. A 27 (1994) L837] for the
three-dimensional Ising model.
