Lattice star and acyclic branched polymer vertex exponents in 3d

Abstract

Numerical values of lattice star entropic exponents and star vertex exponents 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 confirm and improve on estimates in the literature. We also estimate the entropic exponents of a few acyclic branched lattice networks with comb and brush connectivities. In particular, we confirm within numerical accuracy the Duplantier scaling relation for a comb and two brushes.