Field Theory for the Statistics of Branched Polymers, Gelation, and Vulcanization

This paper presents a field theory for the statistics of branched polymers and for the gelation transition. The gelation transition with ΛₚΛL=m, where Λₚ and ΛL are the fugacities for polymer number and loop number, is shown to be in the same universality class as the m-state Potts model. A new fixed point governing the statistics of branched polymers in the dilute limit (Λₚ=0) in 6-ε dimensions with ν=1/2+0.092ε and η=-0.073ε is located. An old result of Zimm and Stockmayer for the radius of gyration of a Gaussion branched polymer is rederived.