  Based on the coalescence model, we analyse the light-nuclei production near
the critical point by expanding the phase-space distribution function
$f(\mathbf{r},\mathbf{p})$ in terms of the phase-space cumulants $\sim \langle
r^m p^m\rangle_c$. We show that the dominant contribution of the phase-space
distribution to the yield of light nuclei is determined by the second-order
phase-space cumulants. Here, we identify the fireball size, the homogeneity
length, and the effective temperature, which are encoded in the second-order
phase-space cumulants, as the relevant scales in explaining the yield of light
nuclei. These scales are typically much larger than the correlation length of
the critical fluctuations created in the rapid expansion of the heavy-ion
systems, so we need to eliminate this dominant contribution of the relevant
scales in order to isolate the critical contribution from the yield of light
nuclei. We find that the second-order phase-space cumulants appeared in the
yields of light-nuclei with different mass numbers share a similar structure.
This property allows us to construct ratios of light-nuclei yields in
appropriate combinations so that the effect of the relevant scales of the
light-nuclei yield cancels, which isolates the critical effects.
