  We have used an effective model of ferroelectric PbTiO$_{3}$, which displays
a representative soft mode-driven phase transition, to investigate how
different features of the potential-energy surface affect the transition
temperature $T_{\rm C}$. We find that the energy difference between
PbTiO$_{3}$'s high-symmetry (cubic) and low-symmetry (tetragonal) phases (which
we call ground state energy $E_{gs}$) is the parameter that most directly and
strongly determines $T_{\rm C}$. We have also found that other simple features
of the energy landscape, such as the amplitude of the distortion connecting the
high-symmetry and low-symmetry structures, can be used as a predictor for
$T_{\rm C}$ only as long as they are correlated with the magnitude of $E_{gs}$.
We discuss how our results relate to the expected behaviors that can be derived
from simpler theoretical approaches, as well as to phenomenological studies in
the literature. Our findings support the empirical rule for estimating $T_{\rm
C}$ proposed by Abrahams et al. [Physical Review 172, 551 (1968)] and clarify
its physical interpretation. The evidence also suggests that deviations from
the expected behaviors are indicative of complex lattice-dynamical effects
involving strong anharmonic interactions (and possibly competition) between the
soft phonon driving the transition and other modes of the material.
