  The dynamics of first order phase transitions are studied in the context of
(3+1)-dimensional scalar field theories. Particular attention is paid to the
question of quantifying the strength of the transition, and how `weak' and
`strong' transitions have different dynamics. We propose a model with two
available low temperature phases separated by an energy barrier so that one of
them becomes metastable below the critical temperature $T_c$. The system is
initially prepared in this phase and is coupled to a thermal bath.
Investigating the system at its critical temperature, we find that `strong'
transitions are characterized by the system remaining localized within its
initial phase, while `weak' transitions are characterized by considerable phase
mixing. Always at $T_c$, we argue that the two regimes are themselves separated
by a (second order) phase transition, with an order parameter given by the
fractional population difference between the two phases and a control parameter
given by the strength of the scalar field's quartic self-coupling constant. We
obtain a Ginzburg-like criterion to distinguish between `weak' and `strong'
transitions, in agreement with previous results in (2+1)-dimensions.
