  We show by a detailed study of the mean-field approximation, the Gaussian
approximation, the perturbation expansion, and the field-theoretic
renormalization-group analysis of a $\varphi^{3}$ theory that its instability
fixed points with their associated instability exponents are quite probably
relevant to the scaling and universality behavior exhibited by the first-order
phase transitions in a field-driven scalar $\phi^4$ model below its critical
temperature near their instability points. Finite-time scaling and leading
corrections to scaling are considered. We also show that the instability
exponents of the first-order phase transitions equal those of the Yang--Lee
edge singularity and employ the latter to improve our estimates of the former.
The outcomes agree well with existent numerical results.
