Bifurcation and stability analysis for phase transitions in the presence of an intermediate state: A general solution

Abstract

A parametric description of phase transitions is done by using general analytical methods involving the bifurcation (branching) of solutions of nonlinear equations in a closed analytical form. The models include an order parameter in the Landau-type kinetic potential, and have been developed to study the impact of both asymmetry and external field on phase transitions in the presence of an intermediate state. General analytical solutions, their stability, and the realization of different transition scenarios in the whole parameter plane divided into three and four regions, respectively, which admit different numbers of distinct physically acceptable solutions, are discussed. The mean transition time between stable liquid and crystalline phases in the region of coexistence of two liquid states is obtained. In particular, the results are analyzed in comparison with generic models of the intrinsic transition dynamics and transition dynamics in the presence of heterogeneity (clusters), when the kinetic potential contains a unitary coefficient of asymmetry. Asymptotic representations of the entire set of parametric dependences are also obtained and analyzed.