Parity of the weak Fréedericksz transition

Motivated by the recent experimental findings by Kumar et al. (Phys. Rev. E., 82, 011701 (2010)) in which the inverse Fréedericksz transition is observed, we have theoretically investigated the parity and the stability of the equilibrium configurations of a Fréedericksz cell with weak planar boundary conditions. Within the one-constant approximation of the Frank theory, the bulk equilibrium equation reduces to the nonlinear pendulum equation. Its solutions, when combined with boundary conditions deriving by the energy anchoring, lose uniqueness, exhibiting various symmetries. Thus, at a given anchoring strength and applied field, the cell becomes a system with metastable discrete energy levels. Our analysis proposes an explanation of the experimental results.