RENORMALIZATION GROUP-APPROACH TO CRITICAL DYNAMICS NEAR THE NEMATIC-SMECTIC-A PHASE-TRANSITION IN LIQUID-CRYSTALS

The dynamics near the nematic to smectic-A phase transition is investigated by the renormalization group method. A simplified model based on a recent mode-coupling calculation on NA transition is analyzed. Anisotropic scaling is considered and the recursion relations for the viscosity coefficients in the liquid crystal gauge for K//1 yields infinity , are obtained, correct to first order in epsilon equals 4 minus d. The dynamic exponent is found to be z equals d/2 plus mu // parallel /2 where d is the dimensionality of the system and mu // parallel is a static exponent. The kinetic coefficients are also expressed entirely in terms of static exponents.