Critical behavior of heat capacity at the smectic-${\mathit{C}}_{\mathrm{\alpha }}^{\mathrm{*}}$–smectic-A transition of the antiferroelectric liquid crystal methylheptyloxycarbonylphenyl octyloxybiphenyl carboxylate (MHPOBC)

High resolution ac calorimetric measurements have been carried out near the smectic-${\mathit{C}}_{\mathrm{\alpha }}^{\mathrm{*}}$–smectic-A phase transition in an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl4’-octyloxybiphenyl-4-carboxylate. A clear deviation from the extended mean-field Landau behavior was seen. The data have been analyzed using a renormalization-group expression, including the correction-to-scaling terms. It was found that the heat capacity anomaly is described well with the three-dimensional XY model, in agreement with the theoretical prediction. It was also found that the second-order correction terms play quite an important role.