Spectrum of the Propagative Modes Near the Smectic-A to Hexatic-B or Crystal-B Phase Transition

Abstract

Near second order or weakly first order phase transitions the sound spectrum of liquids, liquid crystals and crystals usually shows very pronounced anomalies. The order-parameter modulus S, which describes the degree of ordering in the more ordered phase (and is zero in the less ordered phase), becomes soft near the phase transition. That means, the restoring force acting on δS, the deviation of the order-parameter modulus from its equilibrium value, gets weak (and the dynamics slow) close to the phase transition. Thus, instead of being a fast microscopic variable well inside a phase, δS is a slow and macroscopic variable near the phase transition.¹ Its correlation function even diverges at the transition point, T = T _c , in the limit, frequency ω→0. Thus, these huge fluctuations give rise to an additional mechanism of dissipation. This is seen as a cusp-like increase of sound absorption with the peak near T _c and a peak height ~ ω ⁻². In addition, being a macroscopic variable now, δS couples to other scalar variables, like density variations, δρ, and entropy variations, δσ, statically.² Obviously, this also changes the sound velocity, which indeed exhibits very often a dip near T _c .