Exact enumeration and ergodicity in the branched polymer growth model

All bond trees up to size 14 of the branched polymer growth model (BPGM) are exactly enumerated on a square lattice. Each bond tree is topologically classified according to its number of monomers with functionality 2 and 3 (for linear and bifurcated polymerization processes, respectively) and the number of contacts. The associated generating function has growth constant μ=3.01(4) and critical exponent g=0.36(6). Ergodicity violation is discussed in the context of some Monte Carlo implementations. The conflict of birth precedence, generated by interacting growing tips carrying the same chemical distance, is investigated and the results are used to find the correct way the simulations should be performed. We also indicate how the order parameter can be expanded in a series using the enumeration results together with a weight prescription.