Lattice star and acyclic branched polymer vertex exponents in 3d

Abstract

Abstract Numerical values of lattice star entropic exponents γ f , and star vertex exponents σ 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 ϵ-expansion and confirms and improves on estimates in the literature. We also estimate the entropic exponents γ G of a few acyclic branched lattice networks with comb and brush connectivities. In particular, we confirm within numerical accuracy the Duplantier scaling relation γ G − 1 = ∑ f ⩾ 1 m f σ 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 σ f .