Critical behavior of randomly branched polymers with quenched branchings

Randomly branched polymers with quenched branchings, in which monomers interact with each other through the excluded volume interaction, are investigated by using an approach of conformation-space renormalization group theory combined with the replica technique. The perturbation expansion for the mean-square radius of gyration is found and the scaling variable is identified. The renormalization group analysis shows that the critical exponents of the radius of gyration ({ν}=1/4+{ε}/40) and of the total number of configurations ({θ}=5/2-3{ε}/20) no longer obey the scaling law {θ}-1=(D-2){ν}, where {ε}=8-D and D is the space dimensionality, which is tenable for randomly branched polymers with annealed branchings.