Unification of the standard and gradient theories of phase transition

TL;DR

This paper unifies the standard and gradient theories of phase transition by extending the model to include higher powers of the order parameter and its gradient, enabling the description of complex inhomogeneous structures.

Contribution

It introduces a generalized gradient model incorporating fourth powers of the order parameter and its gradient, unifying different phase transition theories.

Findings

Unified description of phase transitions using the generalized model.

Ability to describe spatially inhomogeneous order parameter distributions.

Relevance to nonlinear models with defect structures.

Abstract

We show, that the standard model of phase transition can be unified with the gradient model of phase transitions using the description in terms of the gradient of order parameter. The generalization of the gradient theory of phase transitions with regard to the fourth power of the order parameter and its gradient is proposed. Such generalization makes it possible to described wide class of phase transitions within a unified approach. In particular it is consistent with the nonlinear models, that can be used to describe a phase transition with the formation of spatially inhomogeneous distribution of the order parameter. Typical examples of such structures (with or without defects) are considered. We show that formation of spatially inhomogeneous distributions of the order parameter in the course of a phase transitions is a characteristic feature of many nonlinear models of phase transitions.