Critical exponents for simple non-uniform polymer networks

The authors study a number of non-uniform specified topologies and show rigorously that for certain topologies with cut edges, the critical exponent gamma _t is in agreement with a conjecture given by Gaunt et al. (1984) and that the exponent nu _t= nu , the exponent for self-avoiding walks. The authors also find that the scaling relations gamma _t- gamma _t¹ and gamma _t- gamma _t¹¹ are the same as for self-avoiding walks, previously conjectured only for uniform networks. By assigning an interaction energy to a nearest neighbour contact, they prove that the collapse transition for these topologies is the same as that for self-avoiding walks.