  When a stable ordered phase and a metastable disordered phase are separated
by a flat interface, the metastable state changes to the stable state through
the propagation of the interface. For cases in which latent heat is generated,
the interface displacement during some time interval is proportional to the
square root of the time interval when the extent of supercooling is less than a
certain value. We demonstrate this behavior by deriving a perturbative solution
for a propagating interface in the phase field model. We calculate the
leading-order contribution explicitly, and find that the interface temperature
deviates from the equilibrium transition temperature in proportion to the
interface velocity.
