Symmetry of Nematic Phase and Oblique Axial Order

Abstract

Nematic order is usually described by a uniaxial order parameter, or occasionally by a biaxial order parameter together with the uniaxial one, in a typical configuration. In a general case of a system exposed to two different types of external fields, e.g., an electric field and a magnetic field, an additional order parameter, here called an oblique axial order parameter, is shown to be necessary, in addition to the above order parameters, to describe transition phenomena of the system correctly. The symmetry of the phase with the triplet of the order parameters is discussed. Effect of the oblique axial order are demonstrated practically in two phenomena: (i) qualitative change of the phase transition when the oblique axial order is neglected; (ii) disappearance of phase transition between ordered phases with different ordering axes when an oblique axial field conjugate to the oblique axial order parameter exists.