Phenomenological theory of phase transitions to a state with irregular phase of the order parameter

Abstract

Within the framework of the phenomenological theory of phase transitions with irregular density of Landau potential the formalism is developed to describe the deformed crystal state, in which not only the amplitude of theorder parameter (OP), but also its phase depend upon the spatial coordinate. For multicomponent OP's. corresponding to a multipoint star of the wave vector, we prove that the irregularity can be compensated by introducing a tensor field and constructing a connectivity star. A phenomenological charge of dislocation is introduced to characterize the coupling between the OP and the connectivity. Three possible interpretations of the connectivity field are analyzed. Two of them are shown to be self-contradictory. It is proved that to get a consistent model one should take a pseudoscalar dimension for the phenomenological charge and treat the compensating field as a stress field potential.