Phase transition analogous to Bose-Einstein condensation in systems of noninteracting surfactant aggregates

Ideal bosons and a classical system of monomers that aggregate forming noninteracting ring polymers are known to have the same partition function. So, the ring polymers have a phase transition, the analogue of Bose-Einstein condensation of bosons. At this phase transition macroscopic polymers are formed. The link between these systems is made via Feynman's path integrals: these integrals are the same for the trajectories of the bosons in imaginary time and for the configurations of the polymers. We show that a transition of this general form occurs within a whole class of aggregating systems. Examples are the lamellae formation in suspensions of disclike micelles or the emulsification failure observed in water-oil-surfactant emulsions. As with bosons, the transition occurs even when aggregates do not interact. The lambda-transition in 4He is believed to be Bose-Einstein condensation modified by interatomic interactions. We suggest that interaggregate interactions too only modify the transition we have found.