Fluctuation-driven 1st-order isotropic-to-tetrahedratic phase transition

Motivated in part by recent experiments on liquid crystals with bent-core molecules, which are observed to display a spontaneous chiral symmetry breaking, we introduce a field theory of a 3rd-rank tensor order parameter Tⁱʲᵏ to describe the isotropic-to-tetrahedratic phase transition that we predict to take place in these materials. We study the critical properties of the corresponding phase transition and find that this transition, continuous at the mean-field level, is generically driven 1st-order by thermal fluctuations.