Theory of the smectic A-smectic C phase transition

A second order smectic A-smectic C phase transition in a 3D space has been analyzed by the renorm-group technique. The Frank moduli considered in the one-loop approximation have been shown to remain stable, which is valid for the region 7<ln(103/τ)<102 (τ is the dimensionless vicinity to the transition point). The critical indices describing temperature-variation of the compression modulus of smectic layers, susceptibility and heat capacity are calculated. The indices of the Frank moduli are found in a two-loop approximation. The isotropic critical point is shown to be stable.