Decay of the metastable phase in d=1 and d=2 Ising models

We calculate perturbatively the tunneling decay rate $\Gamma$ of the metastable phase in the quantum d=1 Ising model in a skew magnetic field near the coexistence line $0<h_{x}<1, h_{z}\to -0$ at T=0. It is shown that $\Gamma$ oscillates in the magnetic field $h_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2 Ising model at $T<T_c$, we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We find also evidence for the discrete-lattice corrections in this metastable phase free energy.Comment: 4 pages, REVTe

Dipolar and Quadrupolar Ordering in Ferroelectric Liquid Crystals

The influence of molecular biaxiality on the ferroelectric properties of smectics C$^*$ is considered in detail using both phenomenological and molecular-statistical approaches. We present the generalized Landau-de Gennes theory of the ferroelectric C$^*$ smectics in which the free energy is expressed in terms of the spontaneous polarization, the tilt and the biaxial order parameter, which characterizes the quadrupolar ordering of the molecular short axes. From the microscopic point of view the quadrupolar ordering corresponds to the biaxial ordering of flat molecular cores in the smectic C phase. The interaction between the dipolar and quadrupolar order parameters and the tilt results in the additional temperature dependence of the spontaneous polarization, static dielectric constant and the helical pitch in the broad vicinity of the smectic A-smectic C transition point. The general density-functional theory of the ferroelectric ordering in the smectic C$^*$ phase is also developed taking into account both polar and nonpolar ordering of the short molecular axes. The theory enables one to obtain simple equations for the spontaneous polarization and the biaxial order parameter. These results are used to explain the strong temperature variation of the ratio of the spontaneous polarization and the tilt angle, which has been observed in some ferroelectric liquid crystals. It is also shown that the absolute value and the sign of the spontaneous polarization must be very sensitive to the orientation of the transverse electric and steric dipoles with respect to the flat molecular core

Nonlinear Switching in Surface Stabilized Ferroelectric Liquid Crystals

Dynamics of director field switching in the vicinity of the SmA-SmC$^{*}$ phase transition is studied by means of light scattering. The resonance dependence of scattered intensity on the electric field frequency is observed. The resonance scattering disappears at lower temperatures. The observed anomaly is consistently explained in the framework of the nonlinear kink switching model. The results of this work demonstrate that in the case of materials with high spontaneous polarization this mechanism is predominant

Threshold flexoelectric effect in nematic liquid crystal

Total solution of flexoelectric instability problem is given for finite thickness sample and real elastic moduli