Pattern formation and pattern selection in the Landau–Ginzburg model of critical phenomena

Abstract

In this paper we investigate the family of nonlinear partial differential equations used to describe the kinetics of critical phenomena within the Landau–Ginzburg model. An analysis of the recently obtained symmetry-reduction results for a number of such equations is provided from the point of view of pattern formation at criticality. Various possibilities occur depending on the choice of control parameters. An illustration is provided using several physical examples such as metamagnets and liquid crystals.