  It has been proposed that a first-order phase transition driven to happen in
the metastable region exhibits scaling and universality near an instability
point controlled by an instability fixed point of a $\varphi^3$ theory.
However, this fixed point has an imaginary value and the renormalization-group
flow of the $\varphi^3$ coupling diverges at a finite scale. Here combining a
momentum-space RG analysis and a nucleation theory near the spinodal point, we
show that imaginary rather than real values are physical counter-intuitively
and thus the imaginary fixed point does control the scaling.
