Numerical values of lattice star entropic exponents $\gamma_f$, and star vertex exponents $\sigma_f$, are estimated using parallel implementations of the PERM and Wang-Landau algorithms. Our results show that the numerical estimates of the vertex exponents deviate from predictions of the $\epsilon$-expansion and confirms and improves on estimates in the literature. We also estimate the entropic exponents $\gamma_\mathcal{ G}$ of a few acyclic branched lattice networks with comb and brush connectivities. In particular, we confirm within numerical accuracy the scaling relation $$ \gamma_{ \mathcal{ G}}-1 = \sum_{ f\geq 1} m_f \, \sigma_f $$ for a comb and two brushes (where $m_f$ is the number of nodes of degree $f$ in the network) using our independent estimates of $\sigma_f$.
Categories: cond-mat.stat-mech cond-mat.soft