Inhomogeneous ordered states and translational nature of the gauge group in the landau continuum theory: I. General analysis

Abstract

A phenomenological continuum theory of phase transitions to a global inhomogeneous state of a crystal must take into account the compensating fields that represent the fields of stresses caused by dislocations appearing at the boundaries between local homogeneous regions. These compensating fields, which are introduced in order to satisfy the condition of invariance of the Landau potential with respect to the operation of translation, enter into the theory via extended derivatives of the local order parameters with respect to macroscopic coordinates of the local homogeneous regions in the crystal. Because of this extension of derivatives, the theory of phase transitions to an inhomogeneous state must include the theory of elasticity, in which a potential of the stress field induced by the phase transition is proportional to the compensating field magnitude. The Kröner equation, which describes the state of dislocations induced by spatially inhomogeneous ordering, appears in this theory as a result of minimization of the Landau potential with respect to the compensating fields.