Multicriticality in Hexatic Liquid Crystals

Abstract

A theory is presented for the successive sixfold Fourier components, $C_{6n}$, in the bondorientational order in the neighborhood of a $\mathrm{s}\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{c}-A-\mathrm{h}\mathrm{e}\mathrm{x}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{c}-B$ phase transition. Near the transition we predict that $C_{6n}\sim {C_6^{\sigma }}^n$ with ${\sigma }_n=n+x_{n}n(n-1\mathrm{})\mathrm{}$ where $x_n$ depends weakly on $n$. General arguments are presented for the topology of the phase diagram in the vicinity of the smectic "liquid-hexatic-crystal" triple point which lead to the existence of a tricritical point on the $\mathrm{s}\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{c}-A-\mathrm{h}\mathrm{e}\mathrm{x}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{c}-B$ line.