Mirror symmetry breaking as a problem in dynamical critical phenomena

The critical properties of the Frank model of spontaneous chiral synthesis are discussed by applying results from the field theoretic renormalization group (RG). The long time and long wavelength features of this microscopic reaction scheme belong to the same universality class as multi-colored directed percolation processes. Thus, the following RG fixed points (FP) govern the critical dynamics of the Frank model for d<4: one unstable FP that corresponds to complete decoupling between the two enantiomers, a saddle-point that corresponds to symmetric interspecies coupling, and two stable FPs that individually correspond to unidirectional couplings between the two chiral molecules. These latter two FPs are associated with the breakdown of mirror or chiral symmetry. In this simplified model of molecular synthesis, homochirality is a natural consequence of the intrinsic reaction noise in the critical regime, which corresponds to extremely dilute chemical systems.