  We study critical properties of the relaxation time at a threshold point in
switching processes between bistable states under change of external fields. In
particular, we investigate the relaxation processes near the spinodal point of
the infinitely long-range interaction model (the Husimi-Temperley model) by
analyzing the scaling properties of the corresponding Fokker-Planck equation.
We also confirm the obtained scaling relations by direct numerical solution of
the original master equation, and by kinetic Monte Carlo simulation of the
stochastic decay process. In particular, we study the asymptotic forms of the
divergence of the relaxation time near the spinodal point, and reexamine its
scaling properties. We further extend the analysis to transient critical
phenomena such as a threshold behavior with diverging switching time under a
general external driving perturbation. This models photo-excitation processes
in spin-crossover materials. In the ongoing development of nano-size
fabrication, such size-dependence of switching processes should be an important
issue, and the properties obtained here will be applicable to a wide range of
physical processes.
