  A simplified Ginzburg-Landau theory is presented to study generally a
coupling of a first-order phase transition (FOPT) to a second-order phase
transition (SOPT). We show analytically that, due to the coupling between the
two phase transitions, the SOPT may exhibit a FOPT-like phase separation in
which an ordered phase is separated from a disordered one. This phase
separation results in a distinct behavior in the variation of the order
parameter of the SOPT, namely, it is primarily the proportion of the ordered
phase that contributes to the total order of the whole system during the FOPT.
This growth mode may turn a mean-field critical exponent from 1/2 to 1 or even
bigger.
