A soluble Phase field model.

The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized phase field model, which describes the dynamics of an ordering nonconserved field phi (e.g., solid-liquid order parameter) coupled to a conserved field (e.g., thermal field), After obtaining the rules governing the evolution process, by means of analytical arguments, we present a discussion of the asymptotic time-dependent solutions. The full solutions of the exact self-consistent equations for the model are also obtained and compared with computer simulation results. In addition, in order to check the validity of the present model we compare its predictions with those of the standard phase field model and found reasonable agreement. Interestingly, we find that the system relaxes towards a mixed phase, depending on the average value of the conserved field, i.e., on the initial condition. Such a phase is characterized by large fluctuations of the phi field.