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Various transitions among the phases of isotropic liquid (I), nematic (N) and smectic (SmA, SmC and SmC*) in liquid crystals have been studied extensively. The nematic-smectic A (NA) and the smectic Asmectic C (AC) or the smectic A-smectic C* (AC*) transitions are usually continuous and they are considered to belong to the three-dimensional XY universality class for the critical fluctuations (de Gennes, 1973). Experimentally, this requires a wide range of the nematic phase (Garland & Nounesis, 1994) for the NA transition, whereas at the AC transition the critical fluctuations are very large (Safinya et al., 1980). Ferroelectric liquid crystals exhibiting transitions from the isotropic liquid (I) to the nematic (N), smectic A and the smectic C or smectic C* (with optically active molecules), have also been studied extensively, in particular, those with high spontaneous polarization such as 4(3-methyl-2-chlorobutanoyloxy)4′ -heptyloxybiphenyl (A7). Experimental studies on the ferroelectric liquid crystals with high spontaneous polarization (Bahr & Heppke, 1986Mercuri et al., 2003) have been reported in the literature. The AC (or AC*) transitions in the ferroelectric liquid crystals (Bahr & Heppke, 1990Denolf et al., 2006) and in the antiferroelectric liquid crystals (Ema,, et al., 1996) have also been studied experimentally. Theoretical studies on the AC and AC* transitions have been reported in the literature (Musevic et al.,. 1983Mukherjee, 2009). We have also studied the AC and AC* transitions in the ferroelectric liquid crystals (A7 and C7) theoretically by using the mean field models in our previous works (Salihoglu et al., 1998Yurtseven 2011). Among the various physical properties of the ferroelectric liquid crystals, the dielectric properties have been studied extensively close to the AC (or AC*) transitions (Bahr et al., 1987, Musevic et al., 1983, Yurtseven & Kilit, 2008, Kilit & Yurtseven, 2008, Benguigui, 1984). In an another ferroelectric liquid crystal known as DOBAMBC which shows a second order transition (Zeks, 1984, Indenbom et al., 1976, Carlsson & Dahl, 1983), the AC* transition is associated with an increase in the dielectric constant e⊥ with decreasing temperature, as observed experimentally (Bahr et al., 1987). This increase in the e⊥ has been attributed to the contributions from a soft mode and also a Goldstone mode of this ferroelectric material with

Temperature Dependence of the Dielectric Constant Calculated Using a Mean Field Model Close to the Smectic A - Isotropic Liquid Transition